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Picard variety of a curve; generalized Jacobian; relative Cartier divisors small rational curves; moduli space of vector bundles over a curve Liu, M.: Small rational curves on the moduli space of stable bundles. Int. J. Math. 23, No. 8 (2012)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Mordell-Lang conjecture; semiabelian variety; characteristic \(p\); \(p\)- rank of a quotient Abramovich, D; Voloch, JF, Toward a proof of the Mordell-lang conjecture in characteristic \(p\), Int. Math. Res. Not., 5, 103-115, (1992)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors type of a line bundle on an abelian variety; family of abelian threefolds admitting two principal polarizations Birkenhake Ch., Complex Abelian Varieties., 2. ed. (2004)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Weierstrass semigroup of a point; double covering of a curve; cyclic covering of an elliptic curve DOI: 10.1007/s00574-008-0074-5
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors elliptic curve; Witt ring over elliptic curve; étale cohomology of a curve Arason J. Elman R. Jacob B. On the Witt ring of an elliptic curve (in preparation)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors elliptic curve over the rational function field; ring of invariants; excellent families of elliptic curves; Weyl group; Mordell-Weil lattice of a rational elliptic surface Shioda, T; Usui, H, Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli, 41, 169-217, (1992)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors relative canonical algebra of a fibration
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors extension of an abelian variety by a torus; quotient by a lattice; proper rigid-analytic group M. van der PUT , M. Reversat . '' Construction analytique rigide de variétés abéliennes ''. A paraître. Bull. soc. math. France ( 1989 ). Numdam | MR 1042431 | Zbl 0715.14035
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors anti-Kodaira dimension; rational surface; isolated rational singularities; ample Cartier divisor; minimal resolution; Zariski decomposition of divisors; pseudo effective divisor; dimension formula; anti-genus Sakai, F. Anticanonical models of rational surfaces,Math. Ann. 269(3), 389--410, (1984).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors families of curve singularities; Milnor number of the singularity; generalized criterion for equisingularity
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Artin-Schreier cover; characteristic-\(p\); Cartier operator; \(p\)-rank; \(p\)-torsion; formal patching; wild ramification; \(a\)-number; curve; finite field; Jacobian
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors generalized divisors; generalized line bundles; norm map; compactified Jacobians; Prym variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors projective cone over a polarized variety; first order infinitesimal deformations; deformation of negative weights
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors reduced Grothendieck group; equivariant line bundles on curves; curve over a finite field; resolvent; Stickelberger map; Euler-Poincaré characteristic map; Picard group; tamely ramified Galois covering; class groups 10.1353/ajm.1998.0045
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors conformal field theories of free fermions; bosonization; Jacobian of a compact Riemann surface; formal groups; Hirota tau function; fermion Fock space
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors fundamental group of a curve; \(\ell\)-adic representations; Langlands conjectures; field of rational functions on a curve; Dirichlet series Drinfed, V. G., \textit{two-dimensional \textit{\(\mathcal{l}\)}-adic representations of the fundamental group of a curve over a finite field and automorphic forms on \textbf{GL}(2)}, Amer. J. Math., 105, 85-114, (1983)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors intermediate Jacobian; not finitely generated Griffiths group; Griffiths group of a general cubic sevenfold DOI: 10.1007/BF01459807
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors singular locus of a Schubert variety; Zariski tangent spaces; simply laced algebraic group; geometric quotient; quotient by maximal torus; descriptions of the smooth fixed points; rationally smooth fixed points Carrell, James B.; Kuttler, Jochen, Smooth points of \textit{T}-stable varieties in \(G / B\) and the Peterson map, Invent. Math., 151, 2, 353-379, (2003)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors homogeneous divisors; group actions; almost homogeneous variety; two- orbit variety; classification of complete normal two orbit surfaces D. Ahiezer, ''Equivariant completions of homogeneous algebraic varieties by homogeneous divisors,''Ann. Glob. Anal. Geom.,1, 49--78 (1983).
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Brauer groups; \(n\)-Brauer dimension; \(\mathbb Z/n\)-cyclic classes; \(\mathbb Z/n\)-lengths; connected regular projective relative curves; divisors; hot points; finitely-generated extensions of transcendence degree \(1\); Brauer equivalence classes of cyclic algebras; central division algebras E. Brussel and E. Tengan, Division algebras of prime period \( \ell \neq p\) over function fields of \( p\)-adic curves, Israel J. Math. (to appear).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational points; Jacobian of the Fermat curve Tzermias P.: Mordell-Weil groups of the Jacobian of the 5-th Fermat curve. Proc. Amer. Math. Soc. 125, 663--668 (1997)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors embedding abelian varieties into Jacobian variety; Prym varieties; deformation; multiples of the minimal class Izadi, E.: Subvarieties of Abelian varieties, Applications of Algebraic Geometry to Coding Theory, Physics and Computation (Eilat, 2001), NATO Sci. Ser. II Math. Phys. Chem., 36, Kluwer Acad. Publ., Dordrecht, 2001, pp. 207--214.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors L-functions; Beilinson conjecture; Bloch conjecture; Shimura variety; quaternionic algebra; Jacquet-Langlands theory; isogeny between the corresponding parts of the Jacobian varieties; K-cohomology groups; regulator maps D. Ramakrishnan, Higher regulators on quaternionic Shimura curves and values of \(L\)-functions , Applications of algebraic \(K\)-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 377-387.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors degree of a curve; intersection multiplicity; plane algebraic curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors divisor of a differential; Gorenstein curve; desingularisation; ramification divisor; Weierstrass points on a singular curve De Carvalho, C. F.; Stöhr, K. -O.: Higher order differentials and Weierstrass points on Gorenstein curves. Manuscripta math. 85, 361-380 (1994)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational surfaces; fine classification of non-special rational surfaces; quotient of a rational variety F.Catanese - K.Hulek,Rational surfaces in \(\mathbb{P}\)4 containing plane curves, to appear in Ann. Mat. Pura Appl.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of \({\mathbb{C}}^*\)-type Kizuka T. , Rational functions of C \ast -type on the two-dimensional complex projective space , Tohoku Math. J. (2) 38 ( 1 ) ( 1986 ) 123 - 178 . Article | Zbl 0577.14021
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors curves through a singularity; jets; arcs of curve; Nash problem G. Gonzalez-Sprinberg and M. Lejeune-Jalabert, Sur l'espace des courbes trac\'{}ees sur une singularit\'{}e, Progress in Mathematics, 134 (1996), 9--32.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors family of minimal surfaces of general type parametrized by a complete curve A. Weil, Généralisation des functions abéliennes, J. Math. Pures Appl. (9), \textbf{17} (1938), 47-87.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors elliptic and hyperelliptic curves; Jacobian variety; ruled and rational surfaces; exceptional curve; elliptic soliton
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors modular curve; Jacobian variety; Hecke operator Takuya Yamauchi, On \Bbb Q-simple factors of Jacobian varieties of modular curves, Yokohama Math. J. 53 (2007), no. 2, 149 -- 160.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors torsion subgroup of second Chow group; \(K_ 2\)-cohomology; Galois module structure; Bloch-Quillen-formula; Neron-Severi group; Picard variety Colliot-Thélène, J.-L. and Raskind, W.: K 2-Cohomology and the second Chow group, Math. Ann. 270 (1985), 165-199.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Segre class; zeta function; homogeneous ideal; ranks of a smooth variety; duality defect
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors generalized Weierstrass point; Weierstrass semigroup of a pair; Weierstrass semigroup of a point Kang E., Kim S.J.: Special pairs in the generating subset of the Weierstrass semigroup at a pair. Geom. Dedicata 99, 167--177 (2003)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors hyperelliptic divisors; very ample divisor; canonical divisor; adjunction mapping; degree of the fibres of a ruled surface SERRANO F., ''The adjunction mapping and hyperelliptic divisors on a surface'', J. Reine Angew. Math. 381 (1987), 90--109.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors \(S_ 2\); coordinates of a projective variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors principally polarized abelian variety; theta function; Jacobian varieties of hyperelliptic curves and non-hyperelliptic curves; module over of ring of differential operators Cho K., Nakayashiki A., Differential structure of Abelian functions, Internat. J. Math., 2008, 19(2), 145--171
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors moduli of vector bundles on a curve; geometric invariant theory; theta functions; normalization map Esteves, E.: Separation properties of theta functions. Duke Math. J. 98, 565--593 (1999)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors abelian variety; uniformization; existence of a Néron-model
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors smallest complex algebraic variety containing a given semialgebraic set; complexity of algorithm M.-F. ROY, N. VOROBJOV Computing the Complexification of a Semi-algebraic Set, Proc. of International Symposium on Symbolic and Algebraic Computations, 1996, 26-34 (complete version to appear in Math. Zeitschrift).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors zeta-functions; number of rational points; curve over a finite field; Weil-estimates Serre, J.P.: Sur le nombre des points rationnels d'un courbe algébrique sur un corps fini. C. R. Acad. Sc. Paris 296, 397-402 (1983)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors deformation theory of moduli spaces for vector bundles; semistable rank-2 vector bundles on a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors topology of the quotient variety; action of a complex algebraic torus; intersection Betti numbers; symplectic reduced spaces; intersection homology Y. Hu, The geometry and topology of quotient varieties of torus actions, Duke Math. J. 68 (1992) 151--184. Erratum: 68 (1992) 609.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors divisors on a curve; Brill-Noether number; Clifford index
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors minimal degree of a surface containing a closed integral curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors ampleness of divisors on a smooth projective surface; Bordiga surfaces DOI: 10.1007/BF02570459
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors codegree; small degree; class of a projective variety; degree of dual variety; small sectional genus C. Turrini and E. Verderio, Projective surfaces of small class, Geom. Dedicata 47 (1993), 1--14.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors second order theta functions; dual of the Picard bundle; subvarieties of the Jacobian; higher order theta functions
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curvilinear zero-scheme; hyperplane section of a smooth rational curve; higher genus E. Ballico, J. Migliore, Smooth curves whose hyperplane section is a given set of points, Comm. Algebra 18 (1990), 3015--3040.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Cartier operator; superspecial curve; characteristic \(p\); genus; meromorphic differentials; number of Cartier points Baker, M.: Cartier points on curves. Internat. math. Res. notices 7, 353-370 (2000)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Abelian variety over a global field; Tate module; elliptic curve without complex multiplication Zarhin, Yu.G.: Abelian varieties, \ell-adic representations and SL2, Izv. akad. Nauk SSSR, ser. Mat. 43, 294-308 (1979)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors effective cone; symmetric product of a curve; diagonal
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational curve; \(m\)-regular curve; regularity of a curve; extremal secant line
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors tropical schemes; Picard groups; Cartier divisors; idempotent semiring
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors real algebraic curve of genus 2; neutral real component; Jacobian; group law; quartic curve; 2- and 3-torsion points Fichou, G.: Loi de groupe sur la composante neutre de la jacobienne d'une courbe réelle de genre 2 ayant beaucoup de composantes réelles. Manuscripta math. 104, 459-466 (2001)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors isomorphisms among monodromy groups; lattices in \(PU(1,2)\); congruence subgroups; monodromy groups; Picard-Fuchs equations; hypergeometric functions; discrete groups; volumes of fundamental domains; relative indexes; tables Sauter., J., Isomorphisms among monodromy groups and applications to lattices in \({{\mathrm PU}(1,2)}\), Pacific J. Math.,, 146, 331-384, (1990)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors constructing elements in \(H^1\); self-product of a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors real singular points of a curve; three-point sets of singular points of a unicursal curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors extension class of a vector bundle; holomorphic forms; Albanese variety; families of varieties; infinitesimal invariant
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors blowing-up; Del Pezzo surface; real structure; Picard group; configurations of the real plane quartic curve; anticanonical map; real forms of rational elliptic surfaces without multiple fibres Wall, CTC, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math., 47, 47-66, (1987)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors minimal free resolution; monomial curve; Cohen-Macaulayness; Hilbert function of a local ring; tangent cone
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors existence of a non-singular model for a variety; characteristic zero F.A. Bogomolov and T. Pantev: ''Weak Hironaka Theorem'', Math. Res. Let., Vol. 3, (1996), pp. 299--307.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors torsion zero cycles; Selmer group of the symmetric square; Hyodo-Kato cohomology; selfproduct of a semistable elliptic curve Andreas Langer, Selmer groups and torsion zero cycles on the selfproduct of a semistable elliptic curve, Doc. Math. 2 (1997), 47 -- 59.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors linear series; Gauss map; jacobian of the curve
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Langlands program; automorphic function; complex algebraic curve; principal \(G\)-bundle; Jacobian variety; differential operator; oper
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors complete intersection of three quadrics; intermediate Jacobian; principally polarized abelian variety; Prym variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors non-autonomous cases; rational surfaces; intersection numbers of divisors; algebraic entropy; Picard group Takenawa, T.: A geometric approach to singularity confinement and algebraic entropy. J. Phys. A 34, L95--L102 (2001)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors level curve of a rational function on a smooth algebraic surface; points of indeterminacy; smooth prime curve; rational functions of; \({\mathbb{C}}^*\)-type Kizuka, T.: Rational functions of ?*-type on the two-dimensional complex projective space. Tôhoku Math. J. 38, 123-178 (1986)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors singular curves; rank of a curve; Hurwitz formula Nadia Chiarli, A Hurwitz type formula for singular curves, C. R. Math. Rep. Acad. Sci. Canada 6 (1984), no. 2, 67 -- 72.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Coordinates of a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors projections of the orbit of a given space curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Hasse-Witt-matrix; projective hypersurface; perfect field of characteristic p; Cartier operator; linear variety; generic hypersurface; invertible Frobenius operator DOI: 10.2140/pjm.1972.43.443
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors polar curve; affine plane curve; resolution at infinity of a plane curve; zone de rupture D. Ivanovski, Résolution à l'infini et courbes polaires affines, thèse de l'Université Paul Sabatier à Toulouse sous la direction de Françoise Michel, 2006
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors M-curve; hyperelliptic curve; realisation; gemms; real points of a curve S. M. Natanzon, Automorphisms of the Riemann surface of an \?-curve, Funktsional. Anal. i Prilozhen. 12 (1978), no. 3, 82 -- 83 (Russian).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors deformation of a hyperelliptic curve
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Toric variety; Berkovich space; integral model; metrized line bundle; height of a variety; concave function; Legendre-Fenchel dual; real Monge-Ampere measure José Ignacio Burgos Gil, Patrice Philippon & Martín Sombra, Arithmetic geometry of toric varieties. Metrics, measures and heights, Astérisque 360, Société Mathématique de France, 2014
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors abelian variety; freeness of an ample line bundle on a 3-fold; ample line bundle; isogeny; very ampleness Birkenhake, Ch., Lange, H., Ramanan, S.: Primitive line bundles on abelian threefolds. Manusc. Math.81, 299--310 (1993)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors smooth projective curve; irregular Higgs bundle; spectral sheaf; ruled surface; relative Picard bundle; holomorphic Poisson structure Szabó, Sz., The birational geometry of unramified irregular Higgs bundles on curves, Internat. J. Math., 28, 6, (2017)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors vector bundles over a compact Riemann surface; residue; vector bundles admitting a logarithmic connection; pullback of line bundles; Picard group of moduli space of logarithmic connection; functions on the moduli space; compactification; torsor; Kodaira-Iitaka dimension; Fano three-folds; numerically effective tangent bundle I. Biswas, N. Raghavendra, Line bundles over a moduli space of logarithmic connections on a Riemann surface, Geom. Funct. Anal., in press
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors complete intersection; low codimensional submanifold; dual variety; normal bundle; Chern classes; positive vector bundle; defect of a projective variety Holme, A., A combinatorial proof of the duality defect conjecture in codimension 2, Discrete math., 241, 1-3, 363-378, (2001)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors k-connected graphs; orthogonal representation of a graph; irreducible algebraic variety Lovász, L.; Saks, M.; Schrijver, A., Orthogonal representations and connectivity of graphs, Linear Algebra Appl., 114/115, 439-454, (1989)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors vector bundle on a relative curve; Sophie Germain primes; density H. Brenner. On a problem of Miyaoka. In Number Fields and Function Fields--Two Parallel Worlds, Progress in Math. 239, Birkhäuser, 51-59 (2005).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors quadratic form; Witt ring; fundamental ideal; Pfister form; Witt index; higher Witt indices; generic splitting; height of a quadratic form; stable birational equivalence; Chow motif; Tate motif; Rost motif; homogeneous variety; Rost's nilpotence theorem; Steenrod operation; motivic equivalence Kahn, B., \textit{formes quadratiques et cycles algébriques [d'après rost, Voevodsky, vishik, karpenko ...], exposé bourbaki no. 941}, Astérisque, 307, 113-163, (2006)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors algebraic cycles; algebraic Poincaré polynomial; moduli stack; algebraic cohomology; vector bundles on a smooth curve; Jacobian; smooth flip; Hodge conjecture Balaji, V., King, A.D., Newstead, P.E.: Algebraic cohomology of the moduli space of rank 2 vector bundles on a curve. Topology 36, 567--577 (1997)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors small degrees; rational chain connection; length of rational curves; extremal contractions; divisors; algebraic Sard theorem; Picard number ] Yasuyuki Kachi, Characterization of Veronese varieties and the Hodge index theorem, (unpublished), 1999.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors orbits of a maximal torus on a flag space; basis of the homologies; algebra of invariants; Weyl group; generalized Schubert cocycles; Schubert cells Klyachko, A, Orbits of a maximal torus on a flag space, Funktsional. Anal. i Prilozhen., 19, 77-78, (1985)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Veronese variety; Normal rational curve; Nucleus; Pascal's triangle; Multinomial coefficients; survey; nuclei of Veronese varieties; invariant subspaces of normal rational curves Havlicek H (2003) Veronese varieties over fields with non-zero characteristic: a survey. Discrete Math 267:159--173
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors nef cone; pseudoeffective cone; semistability; cone of curves; fibre product of projective bundle over a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rank of abelian variety; function fields; elliptic curve Pacheco, A.: The rank of abelian varieties over function fields. Manuscripta Math. 118, 361--381 (2005)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors model of a curve; ordinary curve; cyclic quotient singularity; wild ramification; arithmetical tree; resolution graph; component group Néron model D. Lorenzini, Wild models of curves. Algebra Number Theory 8(2), 331-367 (2014)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors real projective variety; degree; central projection; relative orientation; wall-crossing; conservation of numbers
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Theta divisor on Jacobian; dimension of the singularity locus; characterizing Jacobians of hyperelliptic curves among all principally polarized abelian varieties; principally polarized abelian variety
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors associated fan of toric variety; rank of the Picard group M. Eikelberg, Picard groups of compact toric varieties and combinatorial classes of fans, Results Math. 23 (1993), 251--293.
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Fermat surfaces; Hasse-Witt matrix of a Fermat variety; Fermat curves K. TOKI, On Hasse-Witt matrices of Fermat varieties, Hiroshima Math. J. 18 (1988), 95-111
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors Picard group; nonhyperelliptic curve; generalized theta divisor Brivio, Sonia; Verra, Alessandro, The theta divisor of \({\mathrm SU}_C(2,2d)^s\) is very ample if \(C\) is not hyperelliptic, Duke Math. J., 82, 3, 503-552, (1996)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve; Jacobian; Prym variety; abelian variety; \(p\)-rank; supersingular; moduli space; Kummer surface
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors moduli space of semistable vector bundles of rank two on a non-singular curve; Brill-Noether theory Teixidor i Bigas, M.: Brill-Noether theory for vector bundles of rank 2. Tôhoku Math. J.43, 123--126 (1991)
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors action of a cyclic group; \(\ell \)-adic cohomology group of an algebraic curve; Lefschetz fixed point formula
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Picard variety of a curve; generalized Jacobian; relative Cartier divisors minimal basis of the defining prime ideal of a curve; defining equations; projective monomial curves; binomials
0