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simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic \(K\)-theory; values of \(L\)-functions; Beilinson conjecture; finite dimensional representations of graded pro-Lie algebra; polylogarithms; Bernoulli numbers; Riemann zeta-function; generic functional equation; trilogarithm; Bloch-Wigner function; Spence-Kummer relation; motivic cohomology; characteristic classes; Dedekind zeta function; number field; dilogarithm; regulator map; Deligne-Beilinson cohomology; mixed Tate category; Tannakian categories; duality of configurations; Grassmannian trilogarithm M. Prausa, \textit{epsilon: A tool to find a canonical basis of master integrals}, arXiv:1701.00725 [INSPIRE]. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. von Neumann algebra; finite; Grassmannians; affine coordinates | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert modular groups; Hilbert modular varieties; quartic fields H. G. Grundman, Hilbert modular varieties of Galois quartic fields, J. Number Theory 63 (1997), no. 1, 47 -- 58. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. ring of invariant functions; primary invariants Kempf, G.R.: Computing invariants. In: Invariant Theory. Lect. Notes in Math., vol. 1278, pp. 81--94. Springer-Verlag, Berlin (1987) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. degenerations of surfaces of general type; number of singularities; number of components; index of singularity Lee, Y., Numerical bounds for degenerations of surfaces of general type, International Journal of Mathematics, 10, 79-92, (1999) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. mass formulas; local Galois representations; quotient singularities; dualities; McKay correspondence; equisingularities; stringy invariants | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Mots; words; trees; permutations; toric variety; Weyl chambers; semigroups; Lie algebra; Burnside problem for semigroups; symmetric group; skew tableaux; hypermaps; combinatorial theory; representations; continued fractions; differential algebra; probability measures; grammars of zigzags; complexity; finite automaton M. Lothaire , Mots . Hermès Paris 1990 . MR 1252659 | Zbl 0862.05001 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. action of Laplacian; Hodge type decomposition; Kac-Moody-Lie algebra; chain complex; flag variety | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semi-log-canonical singularities; components of moduli schemes Michael A. van Opstall, Moduli of products of curves, Arch. Math. (Basel) 84 (2005), no. 2, 148 -- 154. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. central simple algebras; generalized Severi-Brauer varieties; Chow groups and motives Zhykhovich, M., \textit{decompositions of motives of generalized Severi-Brauer varieties}, Doc. Math., 17, 151-165, (2012) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. recovery of vanishing cycles; log geometry; Riemann-Hilbert correspondence; integral structure of the degenerate variation of mixed Hodge structure S. USUI, Recovery of vanishing cycles by log geometry, Tôhoku Math. J., 53 (1) (2001), pp. 1-36. Zbl1015.14005 MR1808639 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. ring of invariants; action of finite group; prime characteristic; Steenrod algebra; modular invariants; Molien's theorem; Shepard-Todd theorem; polynomial rings; Cohen-Macaulay rings L. Smith, Polynomial Invariants of Finite Groups, A.\ K. Peters, Wellesley, 1995. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hodge ring of an Abelian variety; divisor classes; Hodge conjecture; Hilbert modular surface Fumio Hazama, ''Algebraic cycles on certain abelian varieties and powers of special surfaces'', J. Fac. Sci. Univ. Tokyo Sect. IA Math.31 (1985) no. 3, p. 487-520 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. unirationality for conic bundles; rational point; rational conic bundle surfaces; finite dimensional central simple algebras; large arithmetic fields Yanchevskiĭ, V. I., Astérisque, 209, 311-320, (1992), Soc. Math. France, Paris | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. proper morphisms; universally one-equicodimensional schemes; finite generation of subalgebras Adrian Constantinescu. Proper morphisms and finite generation of subalgebras. II. Universally 1-equicodimensional rings and schemes. Stud. Cerc. Mat., 38(5):438--454, 1986. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. liaison; arithmetically Cohen-Macaulay subschemes; Cayley-Bacharach theorem; Hilbert functions of linked subschemes E. D. Davis, A. V. Geramita, and F. Orecchia, ''Gorenstein Algebras and the Cayley-Bacharach Theorem,'' Proc. Am. Math. Soc. 93(4), 593--597 (1985). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. reductive algebraic group schemes; tilting modules; good filtrations; support varieties; cells of affine Weyl groups; nilpotent orbits Cooper, B. J., On the support varieties of tilting modules, J. Pure Appl. Algebra, 214, 1907-1921, (2010) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine curve; algebraic connection on the trivial bundle; Riemann-Hilbert correspondence; representation of the fundamental group; prescribed monodromy | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. polar varieties; equidimensional varieties; singularities; stratifications; Whitney stratifications; Whitney conditions; tubular neighborhoods; tangent cones; limits of tangent spaces; conormal spaces; projective duality, multiplicity; Nash modifications; Plücker-type formulas; Todd's formulas; characteristic classes; Chern classes | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Categorification; quantum groups; Lie algebras; canonical bases; flag varieties I. Frenkel, M. Khovanov and C. Stroppel, \textit{A categorification of finite-dimensional irreducible representations of quantum sl(2) and their tensor products}, \textit{Selecta Math. (N.S.)}\textbf{12} (2006) 379431 [math/0511467]. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. division algebras; tensor products; Schur indices; ramification; Picard groups; Brauer groups; products of curves; domains Louis Rowen and David J. Saltman, Tensor products of division algebras and fields, J. Algebra 394 (2013), 296 -- 309. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. rational representations; semisimple group; exceptional representations; simple groups; singularities Brion, M., Représentations exceptionnelles des groupes semi-simples, Ann. sci. école. norm. sup., 18, 4, 345-387, (1985) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. discriminant quadratic form; weakly distinguished basis; Milnor lattices of hypersurface singularities; Dynkin diagrams; elliptic hypersurface singularities; action of the braid group; bimodular singularities W. Ebeling : Milnor lattices and geometric bases of some special singularities . L'Enseignement Math. 29 (1983) 263-280. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite morphisms; multiplicity; Rees algebras; singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. flatifying blowing-up; maximal Cohen Macaulay module; simultaneous partial resolution; small resolution; rational double point; RDP; matrix factorization; deformation of algebras; deformation of rational singularities; deformations of exceptional module; partial resolution; domination of resolution; contracting curves; strict transform; Wunram module; blowing up | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Gel'fand pair; Lie groups; Poisson algebras O. S. Yakimova, Saturated commutative homogeneous spaces of Heisenberg type, Acta Applicandae Math. 81 (2004), 339--345. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. surfaces isogenous to a product of curves; surfaces of general type; groups of small order; MAGMA's library Bauer, I.; Catanese, F.; Grunewald, F., The classification of surfaces with \(p_g = q = 0\) isogenous to a product of curves, Special Issue: In Honor of Fedor Bogomolov. Part 1. Special Issue: In Honor of Fedor Bogomolov. Part 1, Pure Appl. Math. Q., 4, 2, 547-586, (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. separation index of a root system; irreducible root system; Weyl group; Weyl chamber; open dual cone; Dynkin diagram | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. topological invariants of algebraic varieties; homology groups; fundamental groups; Alexander polynomials; Hodge structures; Whitney stratifications; plane curve and normal surface singularities; Milnor fibration; lattice for an isolated hypersurface singularity; integral bilinear forms; weighted projective varieties; mixed Hodge structures; hypersurface complements; cohomology of complete intersections A. Dimca, ''Singularities and Topology of Hypersurfaces'', Universitext, Springer-Verlag, New York, 1992. DOI: 10.1007/978-1-4612-4404-2 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. coherent sheaves; finite length modules; Grothendieck ring of varieties; Hilbert scheme of points; torus actions | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic surface; Euclidean space; symmetry; invariant theory of reflection groups V. F. Ignatenko, ''Algebraic surfaces with an infinite set of skew symmetry planes, I,''Ukr. Geom. Sb., No. 32, 47--60 (1989). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. K3 surface; resolution of singularities; Prym variety; lattice of transcendental cycles; Kuga-Satake-Deligne correspondence Bonfanti, M.: On the cohomology of regular surfaces isogenous to a product of curves with \(\chi ({\mathcal O}_S)=2\). arXiv:1512.03168v1 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. generators of ideal of algebraic set; binary forms; polynomial functions; Hilbert function Weyman, J., The equations of strata for binary forms, J. Algebra, 122, 1, 244-249, (1989) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. double cover; hyperelliptic surface of general type; hyperelliptic fibration; fundamental group; slope; singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. dg-schemes; sheaves of dg-algebras; derived intersection; Koszul duality I. Mirkovíc and S. Riche, Linear Koszul duality, Compos. Math. 146 (2010), no. 1, 233-258. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. deformations of manifold and line bundle; differential graded Lie algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Chowla's conjecture; \(L\)-functions; zeta functions of curves; Carlitz extensions; cyclotomic function fields; abelian varieties over finite fields | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. real singularity; blow analytic homeomorphism; bianalytic isomorphisms; classification of real singularities; arc analytic functions; blow-up; modifications; analytic arcs; Lipschitz map Paunescu, L.: An example of blow analytic homeomorphism. Pitman res. Notes math. Ser. 381, 62-63 (1998) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. survey; mappings of cusp type; singularities Church, P. T.; Timourian, J. G.: Global structure for nonlinear operators in differential and integral equations. I. folds; II. Cusps: topological nonlinear analysis. (1997) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Lie algebra of vector fields; polynomial Lie algebras Бухштабер, В. М.; Лейкин, Д. В., Функц. анализ и его прил., 36, 4, 18-34, (2002) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. arithmetical theory of modular functions; complex multiplication of elliptic functions; FdM 18, 396; modular curves; automorphic representations; \(\ell \)-adic representations; Drinfeld theory; elliptic modules; error-correcting codes; elliptic curves | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. level structures; finite flat group schemes; roots of unity Wake, P, Full level structures revisited: pairs of roots of unity, J. Number Theory, 168, 81-100, (2016) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. smoothness; Noetherian schemes; rigidity; stability; Lie algebras S. M. Skryabin, ''Smoothness, flatness and deformations of subalgebras,''Preprint, Manchester Centre Pure Mathematics (1997). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Azumaya algebras; purity; adjoint groups; group schemes I. Panin, Purity for multipliers, Algebra and number theory, pages 66-89. Hindustan Book Agency, Delhi, 2005. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. classification of Hilbert modular varieties; explicit bounds; discriminant of cubic number field; non-rationality Grundman, H. G.: On the classification of Hilbert modular threefolds. Manuscripta math. 72, 297-305 (1991) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Dwork's conjecture; \(p\)-adic meromorphic continuation; unit root \(L\)-function; algebraic varieties; finite field of characteristic \(p\); arithmetic of modular forms; Gouvêa-Mazur conjecture Wan, D, A quick introduction to dwork's conjecture, Contem Math., 245, 147-163, (1999) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. subgroups of Brauer groups; twists of matrix algebras; Gauss sums; Dirichlet characters Chi W.C., Bull.Austral.Math.Soc 50 pp 245-- (1994) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine algebraic varieties; projective varieties; algebraic schemes; rational algebraic functions; singularities; intersection theory; complete intersections; Gorenstein varieties Kunz, E., Einführung in die algebraische geometrie, (1997), Vieweg Braunschweig/Wiesbaden | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. schemes; Grassmannians; finite-dimensional algebras; moduli spaces; varieties Shipman B. A., Discrete and Continuous Dynamical Systems | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. automorphism groups; derived categories; canonical algebras; coherent sheaves; finite dimensional algebras; selfequivalences; exact functors; weighted projective lines; tubular mutations; braid groups; translations Lenzing, H.; Meltzer, H., The automorphism group of the derived category for a weighted projective line, Comm. Algebra, 28, 1685, (2000) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. gradings of semisimple Lie algebras; Lax operator algebras; integrable systems; spectral parameter on a Riemann surface; Tyurin parameters; Hamiltonian theory; prequantization Sh_UMN_2015 Sheinman, O.K. \emph Lax operator algebras and integrable systems. Russian Math. Surveys, 71:1 (2016), 109--156. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. classification of 3-folds of general type; numerically effective canonical divisor; crepant resolution; canonical models; partial resolution; exceptional prime divisor; terminal singularity; quick singularities M. Reid, \textit{Minimal models of canonical} 3\textit{-folds}, in \textit{Algebraic varieties and analytic varieties (Tokyo, 1981)}, \textit{Adv. Stud. Pure Math.}\textbf{1} (1983) 131, North-Holland, Amsterdam, The Netherlands. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert scheme; tautological bundles; McKay correspondence; Fourier-Mukai functor | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Differential graded Lie-algebras; functors of Artin rings | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. centralizers; exceptional Lie algebras; characteristic two; nilpotent classes; reductive algebraic group; nilpotent orbits; stabilizers; order relation; Springer correspondence; Weyl group; sheets Spaltenstein, N., Nilpotent classes in Lie algebras of type \textit{F}_{4} over fields of characteristic 2, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 30, 3, 517-524, (1984) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. autoequivalences of derived categories; integral functors; Fourier-Mukai; linearised derived categories. Hilbert schemes of points; K3 surfaces --------, Groups of autoequivalences of derived categories of smooth projective varieties, Ph.D. dissertation, Freie Universität, Berlin, 2005. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. graded ideal; minimum distance function; Reed-Muller-type code; Hilbert function; Gröbner bases; Carvalho, Lopez-Neumann and López conjecture Martínez-Bernal, J., Pitones, Y., Villarreal, R.H.: Minimum distance functions of graded ideals and Reed-Muller-type codes. J. Pure Appl. Algebra 221, 251-275 (2017) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. module varieties; regular morphisms; immersions; finitely generated algebras; equivariant morphisms; affine varieties; epimorphisms; minimal singularities; Auslander-Reiten quivers | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simply connected simple algebraic group; algebraic number field; valuations; completion; group of K-rational points; S-arithmetic topology; S-congruence topology; congruence kernel; congruence conjecture; exceptional groups; anisotropic K-group Rapinchuk A S, On the congruence subgroup problem for algebraic groups,Dokl. Akad. Nauk. SSSR 306 (1989) 1304--1307 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. points of finite order; best approximation in rings of algebraic functions; Jacobian | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. derived McKay correspondence; Hilbert scheme; tautological bundle | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes of points; torus action; \((q,t)\)-Catalan numbers; quiver varieties A. Buryak, ''The classes of the quasihomogeneous Hilbert schemes of points on the plane,'' Mosc. Math. J., 12:1, 21--36; http://arxiv.org/abs/1011.4459 . | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. \(\widehat {A}\)-genus; circle action; Lefschetz number of elliptic operators; elliptic operators; loop spaces; modularity; rigidity; Dirac operator on loop space twisted by loop group representations; \(\widehat {\mathfrak A}\)-vanishing theorem; elliptic genera; elliptic modular surfaces; elliptic modular functions Liu, K.: On modular invariance and rigidity theorems. J. Diff. Geom. 41(2), 343--396 (1995) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. derivatives of twists of modular \(L\)-series; \(p\)-adic half-integral weight modular forms; central critical values; class numbers; quadratic fields; orders of Tate-Shafarevich groups; elliptic curve N. Jochnowitz, A \(p\)-adic conjecture about derivatives of \(L\)-series attatched to modular forms, Proceedings of the Boston University Conference on \(p\)-Adic Monodromy and the \(p\)-Adic Birch and Swinnerton-Dyer Conjecture (to appear), CMP 94:13. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. symmetric monodromy groups of singularities; reflection subgroup; complete vanishing lattice; middle homology group of Milnor fibre; vanishing cycles; isolated hypersurface singularities; complete intersection singularities Ebeling W.: An arithmetic characterisation of the symmetric monodromy groups of singularities. Invent. Math. 77(1), 85--99 (1984) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. tensor products of cyclic algebras; division algebras of prime index; division algebras over function fields; cubic divisors; central division algebras; ramification divisors; Brauer groups; exponents Michel Van den Bergh, Division algebras on \?² of odd index, ramified along a smooth elliptic curve are cyclic, Algèbre non commutative, groupes quantiques et invariants (Reims, 1995) Sémin. Congr., vol. 2, Soc. Math. France, Paris, 1997, pp. 43 -- 53 (English, with English and French summaries). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Lusztig algorithm; character sheaves; Ree groups; Suzuki groups; cyclic extensions; disconnected groups; almost characters; Lusztig conjecture; characteristic functions; irreducible characters; finite reductive groups | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hecke operators on Hilbert varieties; estimates of eigenvalues; Hecke ring; Hilbert modular variety; \(\ell\)-adic cohomology; local zeta function; toroidal compactifications; Weil conjecture K. Hatada: On the local zeta functions of compactified Hilbert modular schemes and action of the Hecke rings. Sci. Rep. Fac. Ed. Gifu Univ. Natur. Sci., 18, no. 2, 1-34 (1994). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. symplectic structure; moment map; hyper-Kähler quotients; Dynkin diagrams; vertex algebra; symmetric products; Hilbert scheme of points; Poincaré polynomials; Heisenberg algebra; Morse theory; intersection cohomology H. Nakajima, \textit{Lectures on Hilbert schemes of points on surfaces}, \textit{University Lecture Series}\textbf{18}, American Mathematical Society, Providence RI U.S.A., (1999). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. singularities; affine surface of log-general type; minimal embedded resolution; Euler characteristic; rational cuspidal curve; sequence of multiplicities T. Fenske, Rational cuspidal plane curves of type {(d,d-4)} with {\({\chi}\)(\({\Theta}\)_{V}\(\langle\) D\(\rangle\))\(\leq\) 0}, Manuscripta Math. 98 (1999), no. 4, 511-527. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. polynomial formal groups of degree two; valuation ring; Tate-Oort Hopf algebras; Raynaud orders; Hopf orders Childs, L. N.; Sauerberg, J.: Degree two formal groups and Hopf algebras. Mem. amer. Math. soc. 136, No. 651, 55-89 (1998) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. unitary space; reflection groups; algebra of invariants; basic invariant; canonical system of basic invariants | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Zariski pairs; dihedral coverings; elliptic fibrations; topological type of the embedding; Mordell-Weil groups of elliptic \(K3\) surfaces Hiro-o Tokunaga, A remark on E. Artal-Bartolo's paper: ''On Zariski pairs'' [J. Algebraic Geom. 3 (1994), no. 2, 223 -- 247; MR1257321 (94m:14033)], Kodai Math. J. 19 (1996), no. 2, 207 -- 217. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. cohomological Galois theory; topoi; sites; arithmetic curves; algebraic Teichmüller theory; modular groups; elliptic curves; moduli theory of curves; conformal field theories Grothendieck, Alexandre: La longue marche à travers la théorie de Galois tome 1, (1995) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. local quivers; representations of quivers; dimension vectors; irreducible representations; torus knot groups Adriaenssens J., Le Bruyn L.: Local quivers and stable representations. Comm. Algebra 31(4), 1777--1797 (2003) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. invariants of Hilbert schemes of zero-dimensional subschemes; Betti numbers; Kummer varieties; Chow ring Göttsche, L.: Hilbert schemes of zero-dimensional subschemes of smooth varieties. Lect. Notes Math. vol. 1572, Berlin Heidelberg New York: Springer 1993 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. homology of arithmetic groups; torsion; mod-$p$ modular forms; $L$-functions; analytic torsion | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. threefolds of general type; canonical map; finite group actions | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. \(\mathcal{A}\)-equivalence; characteristic \(p\); parameterized curves; simple singularities of multigerms | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. irreducible characters of Hecke algebras; Jones-Ocneanu trace; equivariant cohomology of sheaves; perverse sheaves; reductive algebraic groups; Hochschild homology; Soergel bimodules Webster, B., Williamson, G.: The geometry of Markov traces. arXiv:0911.4494 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Ulrich modules; special Cohen-Macaulay modules; McKay correspondence; cyclic quotient surface singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Dynkin diagrams; normal quartic surfaces; sextic curves; prescribed singularities; action of the Weyl group on the moduli space Urabe, T.: On quartic surfaces and sextic curves with singularities of type \(\tilde E_8 \) ,T 2, 3, 7,E 12. Publ. RIMS, Kyoto Univ.20, 1185-1245 (1984) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. smoothability; zero-dimensional schemes; Gorenstein algebras; Hilbert scheme J. Jelisiejew, \textit{Local finite-dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable}, J. Algebra App., 13 (2014), 1450056. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. abelian automorphism groups; surface of general type; genus 2 fibrations | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. non-euclidean crystallographic group; compact bordered Klein surface; order of an automorphism; topological type; NEC groups | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. organizing centre of an imperfect bifurcation problem; simple root of an auxiliary operator; inflated mapping; singularities of the germs of smooth mappings | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine algebraic varieties; linear algebraic groups; groups of rational points; Jordan decomposition; conjugacy classes; semi-simple elements | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. cofree algebraic group; coregular algebraic group; finite dimensional representation; complex reductive algebraic group; symmetric algebra; algebra of invariants; real semisimple Lie algebra; compact analytic subgroup Nicolás Andruskiewitsch, On the complicatedness of the pair (\?,\?), Rev. Mat. Univ. Complut. Madrid 2 (1989), no. 1, 13 -- 28. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. projective representations of quivers; varieties of representations; rational smoothness; quantum groups; quantized enveloping algebra | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. characters; false theta functions; Jacobi forms; modular forms; vertex algebras Bringmann, K.; Milas, A., W-algebras, higher rank false theta functions and quantum dimensions, Selecta math., 23, 2, 1249-1278, (April 2017) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Shafarevich-Tate group; Picard groups; transcendental \(j\)-invariant; finite field; algebraic function field; elliptic curve; fibers of the Néron model; irreducible projective curve; Selmer group; embedding | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. normal Gorenstein singularity; cobordism invariants; cobordism group of stably framed 3-manifolds; e-invariant; resolution of singularities; complex analytic surface; Milnor number | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Kähler group; fundamental group of a compact Kähler manifold; Mal'cev completion; quadratic presentations; three-step nilpotent Lie algebras; abelianization; nilpotent fundamental group; characteristic subspace James A. Carlson & Domingo Toledo, ``Quadratic presentations and nilpotent Kähler groups'', J. Geom. Anal.5 (1995) no. 3, p. 351-359, erratum in \(ibid.\)7 (1997), no. 3, p. 511-514 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. simple elliptic singularities; moduli algebras; modulus; Artinian local algebras; \(j\)-invariant Chen, H., Seeley, C., Yau, S.S.-T.: Algebraic determination of isomorphism classes of the moduli algebras of \$\(\backslash\)tilde\{E\}\_\{6\}\$ singularities. Math. Ann. 318, 637--666 (2000) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. K-homology theory; quasiprojective schemes; Riemann-Roch theorem; normal cone; K-groups of reductive group schemes R. W. Thomason, Riemann-Roch for algebraic versus topological \?-theory, J. Pure Appl. Algebra 27 (1983), no. 1, 87 -- 109. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. polynomial rings; covariants; polynomial representations; invariant theory; representation theory of linear groups Green, J. A.: Classical invariants and the general linear group. Progr. math. 95, 247-272 (1991) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. maximal orders; Dedekind domains; separable algebras; reduced norms; traces; localizations; completions; discrete valuation rings; Brauer groups; crossed products; simple algebras; hereditary orders I. Reiner, \textit{Maximal Orders}, London Mathematical Society Monographs. Vol. 28, The Clarendon Press, Oxford University Press, Oxford, 2003. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. punctual Hilbert scheme of a surface; complete flags; singularities A. S. Tikhomirov, ''A smooth model of punctual Hilbert schemes of a surface,''Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],208, 318--334 (1995). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. compactified Jacobians; Hilbert scheme of points; reduced curves with locally planar singularities; perverse filtration; decomposition theorem; support theorem | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. universal extension classes; general linear groups; special linear groups; infinitesimal group schemes; Frobenius kernels; cohomological finite generation | 0 |
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