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Picard variety of a curve; generalized Jacobian; relative Cartier divisors construction of a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors number of rational points; Hasse-principle for a variety; Brauer-Manin obstruction P. Sarnak and L. Wang, ''Some hypersurfaces in \({\mathbf P}^4\) and the Hasse-principle,'' C. R. Acad. Sci. Paris Sér. I Math., vol. 321, iss. 3, pp. 319-322, 1995.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Leech lattice; Mordell-Weil lattice; elliptic curves; function field of a hyperelliptic curve; minimal vectors N. D. Elkies, ''Mordell-Weil lattices in characteristic 2, II: The Leech lattice as a Mordell-Weil lattice,'' Invent. Math., vol. 128, iss. 1, pp. 1-8, 1997.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Jacobian variety; divisors; extremal quasiconformal map; Teichmüller map; Beltrami coefficient
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors pseudomanifold; equivariant cohomology; equivariant Thom-Gysin morphism; rational smoothness; singularity; Schubert variety; action of a torus; equivariant Euler class Arabia, A., Classes d'euler équivariantes et points rationnellement lisses, Ann. Inst. Fourier (Grenoble), 48, 3, 861-912, (1998)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors algebraic curve in \(\mathbb{C}^2\); singular point; critical value; multiplicity of a singular point; transversality; Milnor number; signature of a link; Tristram-Levine signatures Maciej Borodzik, Morse theory for plane algebraic curves, J. Topol. 5 (2012), no. 2, 341 -- 365.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors moduli space of curves of genus g; Picard variety; Poincaré sheaf; stable bundle; polarization by the theta divisor Kempf, G., Rank \(g\) Picard bundles are stable, Am. J. Math., 112, 397-401, (1990)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors isogenies between a generalized Prym variety and spectral Prym-Tjurins; moduli space; Riemann surface; Prym-Tjurin variety R. Scognamillo, Prym - Tjurin varieties and the Hitchin map, Math. Ann. 303 (no. 1) (1995), 47--62.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors CM cycles; Shimura curve; \(p\)-adic integration; anti-cyclotomic \(p\)-adic \(L\)-function; \(p\)-adic formula of Gross-Zagier type; generalized Heegner cycles; \(p\)-adic Abel-Jacobi map M. Masdeu, CM cycles on Shimura curves, and \textit{p}-adic \textit{L}-functions, Compos. Math. 148 (2012), no. 4, 1003-1032.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors motivic orthogonal two-dimensional representations; motives of rank two with a non-degenerate symmetric pairing; diagonal quartic K-3 surface; \(\zeta\)-function of a variety; algorithm; \(p\)-adic Hodge theory Livn\.e, R., Motivic orthogonal two-dimension representations of Gal\(\left(\overline{{\mathbf{Q}}}/{\mathbf{Q}}\right)\), Israel J. Math, 92, 149-156, (1995)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Cartier-Dieudonné theory; sheaf of K-groups; augmented artinian local k-algebras; crystalline cohomology; formal Picard group; Artin-Mazur groups; Witt vector cohomology; Chow group Stienstra, J.: Cartier-Dieudonné theory for Chow groups. J. Reine Angew. Math. \textbf{355}, 1-66 (1985) (correction. J. Reine Angew. Math. \textbf{362}, 218-220 (1985))
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve on a surface; curve of contact; locally Cohen-Macaulay curves M. Boratyński, On the curves of contact on surfaces in a projective space, Algebraic \?-theory, commutative algebra, and algebraic geometry (Santa Margherita Ligure, 1989) Contemp. Math., vol. 126, Amer. Math. Soc., Providence, RI, 1992, pp. 1 -- 8.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors stability of the Poincaré bundle; determinantal variety; moduli space; Hilert polynomials; Jacobian Balaji, V.; Brambila-Paz, L.; Newstead, P. E., Stability of the Poincaré bundle, Math. Nachr., 188, 5-15, (1997)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Jacobian variety; quartic curve; Weierstrass points; Mordell-Weil group; isogeny; CM elliptic curve Matthew J. Klassen and Edward F. Schaefer, Arithmetic and geometry of the curve \?³+1=\?\(^{4}\), Acta Arith. 74 (1996), no. 3, 241 -- 257.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors quadric line complex; Kummer surface; Jacobian of the genus 2 curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors monodromy group of a branched covering; Hurwitz system; cellular decomposition; intersection matrix for the 1-cycles; homology basis; conformal self-mappings of Riemann surfaces; periods; quadratic periods; Abelian integrals; Klein-Hurwitz curve; Fermat curve; homogeneous linear differential equation Tretkoff, [Tretkoff and Tretkoff 84] C. L.; Tretkoff, M. D., Combinatorial group theory, Riemann surfaces and differential equations. contributions to group theory, 467--519, contemp. math., 33., \textit{Providence, RI: Amer. Math. Soc.}, (1984)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors stable reduction; discrete valuation field; Jacobian of hyperelliptic curve; Néron model; group of components; separable field extension; Weil restriction 7. B. Edixhoven, Q. Liu and D. Lorenzini, The p-part of the group of components of a Néron model, J. Alg. Geom.5(4) (1996) 801-813.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Witt ring; Witt functor; Witt equivalence; real closed field; function field of a curve; Scharlau transfer; Scharlau's norm principle; Knebusch-Milnor exact sequence; real holomorphy ring
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve of genus two; simple 2-dimensional abelian variety; rank of Mordell-Weil group
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors very ample invertible sheaf on a curve of genus three; Noether-Enriques- Petri theorem; intersection of quadrics; curves of genus three embedded by complete linear series
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors toric variety; fan; toric ideal; blow-up; desingularization; rational singularity; resolution of singularities; divisors David A. Cox, Toric varieties and toric resolutions, Resolution of singularities (Obergurgl, 1997) Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 259 -- 284.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors linear systems of plane curves; fat point; projection of a nonsingular curve Maria Virginia Catalisano and Silvio Greco, Linear systems: developments of some results by F. Enriques and B. Segre, Geometry and complex variables (Bologna, 1988/1990) Lecture Notes in Pure and Appl. Math., vol. 132, Dekker, New York, 1991, pp. 41 -- 57.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors genus \(\neq 1\); hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; families of curves
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Weierstrass semigroup; double covering of a curve; Hirzebruch surface; normalization of a curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors normal variety defined over a finite field; characteristic roots of the L-function; characteristic roots of the zeta function
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors generic embedding of an elliptic curve in a complex surface Iljashenko, Y. and Pyartli, A. , Neighborhoods of zero type in embedded complex tori . In: Topics in Modern Mathematics. Transl. from Petrovskii Sem. No. 5 (ed. O.A. Oleinik), New York 1985.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Kuga fiber variety; arithmetic variety; field of definition; strong bottom field; class group of a maximal order Abdulali, S.: Conjugation of Kuga fiber varieties, Math. Ann.294, 225-234 (1992).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Galois cohomology; local-global principle; semi-global field; function field of a curve; discrete valuation
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors threefold; family of algebraic 1-cycles; Abel-Jacobi map; intermediate Jacobian; Grothendieck's generalized Hodge conjecture
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve of genus \(g\geq 2\); Coleman-Chabauty bound; upper bound; number of rational points; Jacobian; Mordell-Weil rank
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors product theorem of Nadel; bound for Chern class; Fano variety; movable rational curve Campana, F.: Une version géométrìque généralisée du théorème de produit de Nadel. C.R. Acad. Sci. Paris312, 853-856 (1991)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors modular height; Arakelov metric; Poincaré metric; modular parametrization of a semi-stable elliptic curve; modular curve Abbes, A.; Ullmo, E., Comparaison des métriques d'arakelov et de Poincaré sur \(X_0(N)\), Duke Math. J., 80, 2, 295-307, (1995)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Galois structure; elliptic curves; Hopf orders; principal homogeneous space; explicit determination of generators; group schemes; \(p\)-adic \(L\)-function of an elliptic curve; elliptic units; Picard invariant Cassou-Noguès, Structures galoisiennes et courbes elliptiques, J. Théor. Nombres Bordeaux 7 pp 307-- (1995)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors polynomial; derivative; quartic Diophantine equation; elliptic curve; hyperelliptic curve; Jacobian variety; algebraic surface R. H. Buchholz, J. A. MacDougall, When Newton met Diophantus: A study of rational-derived polynomials and their extension to quadratic fields, J. Number Theory 81 no. 2 (2000) 210-233.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors estimate; number of integral points on a Thue curve; rational points
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors complex uniformization; Mumford curves; Jacobians of a \(p\)-adic Shimura curve; \(q\)-adic modular curves
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Theorems of Pascal and Brianchon; extension; plane curves; surfaces of the third order; Cartesian higher geometriy; conjugated polygons; inscribed into a curve; conic section
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors isolated singularity of a complex curve; algebraic link; plane curve singularities; iterated torus link; positive closed braid; minimal closed braid representative
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve over a finite field; Suzuki group; automorphism group of a curve; maximal curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors topology of a real plane curve; analytic components; real analytic component Cucker, F., Pardo, L. M., Raimondo, M., Recio, T., Roy, M. F.: On local and global analytic branches of a real algebraic curve. Lecture Notes in Computer Science, Vol. 356, 161--182, Berlin, Heidelberg, New York: Springer 1989
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Grassmann variety; Plücker embedding; complex of lines; generalized Hodge conjecture; Fano variety Nagel, J., \textit{the generalized Hodge conjecture for the quadratic complex of lines in projective four-space}, Math. Ann., 312, 387-401, (1998)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors divisors modulo algebraic equivalence; Picard number; complex Fermat surface; generators of the Néron-Severi group N. Aoki and T. Shioda, ``Generators of the Néron-Severi group of a Fermat surface'' in Arithmetic and Geometry, Vol. I , Progr. Math. 35 , Birkhäuser Boston, Boston, 1983, 1-12.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Eisenbud-Goto conjecture; syzygy module; regularity of a curve D. Giaimo, On the Castelnuovo--Mumford regularity of connected curves, Trans. Am. Math. Soc. 358(1), 267--284 (2006) (electronic).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors integral scheme; field of positive characteristic; canonically polarized surface; quotient of an integral scheme by a nontrivial action; adjunction formula; Picard scheme
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rigid analytic torus; quotient of an analytic group by a lattice; extension of an abelian variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Torelli problem; Jacobian; principally polarized abelian variety; Prym variety; Clifford index; intersection of quadrics LANGE (H.) , SERNESI (E.) . - Quadrics containing a Prym-canonical curve , J. Alg. Geom., t. 5, 1996 , n^\circ 2, p. 387-399. MR 96k:14021 | Zbl 0859.14009
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors real algebraic surfaces; Hilbert's 16-th problem; complexification; mutual positions of connected components of a nonsingular plane real algebraic curve of given degree O. Ya Viro, Progress in the topology of real algebraic varieties over the last six years, \textit{Uspekhi Mat. Nauk.}\textbf{41} (1986) 45-67 (in Russian); \textit{Russian Math. Surveys}\textbf{41} (1986) 55-82.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors effective 1-cycles; length of extremal ray curve; Kähler cone; Calabi-Yau 3-folds; Picard number; nef cone; length of divisorial extremal rays Viacheslav V. Nikulin, The diagram method for 3-folds and its application to the Kähler cone and Picard number of Calabi-Yau 3-folds. I, Higher-dimensional complex varieties (Trento, 1994) de Gruyter, Berlin, 1996, pp. 261 -- 328. With an appendix by Vyacheslav V. Shokurov.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors asymptotic values of a real polynomial; Jacobian condition; real Jacobian conjecture Peretz, Ronen: The variety of asymptotic values of a real polynomial étale map, J. pure appl. Algebra 106, 102-112 (1996)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors standard basis; Gröbner basis; syzygies of a canonical curve; equations of Petri's type; non-minimal resolution; reducible canonical curves; Green's conjecture; second syzygy module; Hilbert's syzygy theorem Milnor, J.: On the 3-dimensional Brieskorn manifolds \textit{M(p, q, r)}. In: Neuwirth, L.P. (ed.) Knots, Groups, and 3-Manifolds (Papers Dedicated to the Memory of R. H. Fox), pp. 175-225. Princeton Univ. Press, Princeton, N. J. (1975)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors linearly normal curve; families of curves lying on a smooth cubic surface; reducibility of Hilbert scheme Dolcetti, A; Pareschi, G, On linearly normal space curves, Math. Z., 198, 73-82, (1988)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors hypersurfaces; abelian varieties; canonical maps; Gauss maps; theta divisors; automorphisms of a covering; monodromy groups; generic coverings
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors \(p\)-adic height pairing; Jacobian variety; arithmetic intersection theory; differentials of the third kind; de Rham cohomology R. F. Coleman and B. H. Gross, ''\(p\)-adic heights on curves,'' in Algebraic Number Theory, Adv. Stud. Pure Math. 17, Academic Press, Boston, 1989, 73--81.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve of genus two; rational Weierstrass point; embedding; Jacobian; formal group; theta functions Grant D.: Formal groups in genus 2. J. Reine. Angew. Math. 411, 96--121 (1990)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors regular rigid analytic spaces of finite genus; analytic spaces which are the complement of a compact set in an algebraic curve Liu, Q, Ouverts analytiques d'une courbe algébrique en géométrie rigide, Annales de l'Institut Fourier, 37, 39-64, (1987)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors normal variety; orbit closure; complexity of the action of a reductive group Arzhantsev, I.V.: On the normality of the closures of spherical orbits. Func. Anal. Prilozh. 31(4), 66--69 (1997) (in Russian), English transl.: Func. Anal. Appl. 31, No. 4 (1997), 278--280
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors singularities of a 3-dimensional variety; quadratic transformations
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors orbit space; theta matrix; coverings; Klein curve; Jacobian variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors discrete logarithm problem; hyperelliptic curve cryptography; index calculus; divisor class group; Jacobian variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors projective toric variety; one-parameter subgroup; wall-crossing; semi-orthogonal decomposition; singularity categories; full exceptional collection; GIT; windows; geometric invariant theory; fan structure; bounded derived category of coherent sheaves; equivariant ample line bundle; VGIT; reductive linear algebraic group; variations of GIT structures; birational methods; blow-ups at smooth centres; linearisation of a group action
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors local uniformization of a branch of an algebraic curve; Newton polyhedra
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors hyperplane section; genus; moduli; semicontinuity; non special embeddings in projective 4-space; maximal rank conjecture; embedding of a general smooth curve Ballico, E; Ellia, P, On postulation of curves in \(\mathbb{P}^4\), Math. Z., 188, 215-223, (1985)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curves over a finite field; number of rational points; number of points of degree \(m\); genus; asymptotic behavior; number of effective divisors M. A. Tsfasman, ''Some Remarks on the Asymptotic Number of Points, Coding Theory and Algebraic Geometry,'' in Lecture Notes in Math. (Springer-Verlag, Berlin, 1992), Vol. 1518, pp. 178--192.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors irreducible curve; rational function; number of prime divisors Pappalardi, F.; Shparlinski, I.: On Artin's conjecture over function fields. Finite fields appl. 1, 399-404 (1995)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors the generalized Laguerre polynomials; total symbols of differential operators; the image conjecture; the Jacobian conjecture Wenhua Zhao, A deformation of commutative polynomial algebras in even numbers of variables, Cent. Eur. J. Math. 8 (2010), no. 1, 73 -- 97.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors boundedness conjecture for group of rational torsion points; elliptic curve; Mordell-Weil theorem; abelian variety; potential complex multiplication; torsion points on the Fermat curves; p-adic abelian integrals Coleman, Robert F., Torsion points on curves and \textit{p}-adic abelian integrals, Ann. of Math. (2), 121, 1, 111-168, (1985), MR782557
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors C\({}^{\infty }\) curve germs; ordering in a real variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors genus of a plane algebraic curve; intersections of surface patches; computer graphics; genus of a space curve; Puiseux series Katz S, Sederberg T. Genus of the intersection curve of two rational surface patches. CAGD, 1988, 5(3): 253--258.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors number of divisors; modular curve; cuspidal divisor; Ramanujan sums; Fourier coefficients; Fermat curve [MR]V.K. Murty andD. Ramakrishnan, The Manin-Drinfeld Theorem and Ramanujan Sums, Proc. Indian Acad. Sci. 97 (1987), 251--262.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Betti numbers of a complete symmetric variety; Poincaré polynomial; cellular decomposition; rational points Corrado De Concini and Tony A. Springer, \(Betti numbers of complete symmetric varieties. \)Geometry today (Rome, 1984), 87--107, Progr. Math., 60, Birkhauser Boston, Boston, MA, 1985.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors stratified multiplicative property; Todd-class of a toric variety; Euler characteristic; Ehrhart polynomial S. E. Cappell and J. L. Shaneson, ''Genera of algebraic varieties and counting of lattice points,'' \textit{Bulletin (New Series) Amer. Math. Soc.}, \textbf{30}, No. 1 (1994).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors subcanonical curves on smooth surfaces; space curves; non-complete intersection; existence of effective divisors; Picard group
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Jacobian of Fermat curve; endomorphism ring Lim, C. H.: Endomorphisms of Jacobian varieties of Fermat curves. Compositio math. 80, 85-110 (1991)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational curve parametrization; algebraic curve; degree of an algebraic curve; singularities of an algebraic curve; multiplicity of a point Pérez-Díaz, S., Computation of the singularities of parametric plane curves, J. Symb. Comput., 42, 8, 835-857, (2007)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors \(SU(2)\)-character variety of a Seifert-fibered homology sphere; compact holomorphic orbifold of dimension 2; space of projective unitary representations of the orbifold fundamental group; moduli space of stable parabolic bundles Boden Hans U, Representations of orbifold groups and parabolic bundles, Comment. Math. Helv. 66(3) (1991) 389--447
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors product theorem of Nadel; bound for Chern class; Fano variety; movable rational curve Campana, F. Une version géométrique généralisée du théorème du produit de Nadel,Bull. Soc. Math. France 119(4), 479--493 (1991).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational discs; selfintersection number of an arithmetic curve; filled singularity resolution; Picard modular surfaces; automorphic forms; monodromy group; integrals on Riemann surfaces Holzapfel, R.-P.: Arithmetic curves on ball quotient surfaces, Ann. Glob. Analysis and Geometry 1, o..2 (1983), 21-90.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Riemann surface; jacobian variety; algebraic curve; theta function
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors characteristic \(p\); absolute Frobenius; ordinary curve; étale abelian covering of a generic curve
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Picard group of a linear algebraic group Knop, F., Kraft, H., Luna, D., et al.: Local properties of algebraic group actions, in: Algebraische Transformationsgruppen und Invariantentheorie (H. Kraft, P. Slodowy, T.A. Springer eds.), \textbf{63-76}, DMV Semin., 13, Birkhäuser, Basel-Boston-Berlin, 1989
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors vector bundles on a curve; ruled surfaces; moduli of vector bundles; bisecant curves; trisecant curves; Segre invariants; elementary transformation
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors class group of surfaces in 3-space; curves in threefolds; surface containing a given curve; Pic A. Buium , The automorphism group of a non-linear algebraic group , to appear.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors algebraic curve; tropical curve; Jacobian; Abel map; toric variety
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors number of generators of ideals; Cohen-Macaulay type; Hilbert function of the coordinate ring; minimal free resolution; least degree of a nonsingular curve Geramita, A. V.; Maroscia, P., The ideal of forms vanishing at a finite set of points in \(\mathbb{P}^n\), J. Algebra, 90, 528-555, (1984)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors zero divisors; zero currents for sections of a vector bundle; locally Lebesgue integrable forms; atomic section; divisor of an atomic section; Euler class F. R. Harvey and S. Semmes, Zero divisors of atomic functions , Ann. of Math. (2) 135 (1992), 567--600. JSTOR:
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors defining equations of blow-up algebras; Rees algebras; Cohen-Macaulay domain; jacobian dual of a matrix; generators of the defining ideal DOI: 10.1016/0022-4049(95)00087-9
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors rational elliptic fibration; moduli; ball quotient; homology of cyclic coverings; central extension of a braid class group; Eisenstein curve; rational curves Gert Heckman and Eduard Looijenga, The moduli space of rational elliptic surfaces, Algebraic geometry 2000, Azumino (Hotaka), Adv. Stud. Pure Math., vol. 36, Math. Soc. Japan, Tokyo, 2002, pp. 185 -- 248.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors Hilbert schemes of points on a surface; quasi-modular forms; multiple zeta value; generalized partition
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors curve; cyclic cover; Jacobian; abelian variety; Shimura variety; PEL-type; moduli space; reduction; \(p\)-rank; supersingular; Newton polygon; \(p\)-divisible group; Kottwitz method; Dieudonné module; Ekedahl-Oort type
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors cycle space; Chow variety; \(n\)-convexity; ample normal bundle; topological space of compact \(n\)-cycles; analytic families of cycles; reduction of convexity; Cartier divisor; higher integration maps Barlet, D.: How to use the cycle cpace in complex geometry. Several Complex Variables MSRI Publications, vol. 37, pp. 25--42, 1999
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors polarization; characteristic p; Jacobian variety; supersingular elliptic curves; prescribed automorphism group; curves of genus two; Hasse-Witt- matrix; class numbers of quaternionic algebras T.IBUKIYAMA, T.KATSURA, and F.OORT,\textit{Supersingular curves of genus two and class numbers}, Compositio Math. 57 (1986), no. 2, 127--152.MR827350
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors analytic subset of a real algebraic variety; diffeomorphism
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors germ of a plane real curve; Milnor number
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors filtration in the automorphism group; fundamental group of a smooth irreducible complete curve Oda, T.: A note on ramification of the Galois representation on the fundamental group of an algebraic curve. J. number theory 34, 225-228 (1990)
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors real Jacobian conjecture; centre of a vector field; Hamiltonian vector field
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors canonical model of a Shimura variety; Baily-Borel compactification; \(\ell\)-adic sheaf R. Pink, On \textit{l}-adic sheaves on Shimura varieties and their higher direct images in the Baily-Borel compactification, Math. Ann. 292 (1992), no. 2, 197-240.
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors real zeroes; bound for the number of zeroes of a period; Picard-Fuchs equation G. S. Petrov, ''Number of zeros of complete elliptic integrals,'' Funkts. Anal.,18, No. 2, 73-74 (1984).
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors generalized flag space; variety of Borelian subgroups; Schubert cycles; toric variety; algebra of invariants; arrangement of points Klyachko, A.A.: Toric varieties and flag varieties. Tr. Mat. Inst. Steklova 208, 139--162 (1995) (in Russian), English transl.: Proc. Steklov Inst. Math. 208 (1995), 124--145
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors elliptic curve; differential form; genus one; parity-check matrix; generator matrix; elliptic code over a field of characteristic 2
0
Picard variety of a curve; generalized Jacobian; relative Cartier divisors hyperplane section; genus; moduli; semicontinuity; maximal rank conjecture; embedding of a general smooth curve; non special embeddings in projective 4-space Ballico E., Ellia P.: On postulation of curves in \$\$\{\(\backslash\)mathbb\{P\}\^4\}\$\$ . Math. Z. 188, 215--223 (1985)
0