PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2012 | 10 | 4 | 1306-1313
Tytuł artykułu

The Picard group of a coarse moduli space of vector bundles in positive characteristic

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive characteristic.
Wydawca
Czasopismo
Rocznik
Tom
10
Numer
4
Strony
1306-1313
Opis fizyczny
Daty
wydano
2012-08-01
online
2012-05-31
Twórcy
Bibliografia
  • [1] Beauville A., Laszlo Y., Conformal blocks and generalized theta functions, Commun. Math. Phys., 1994, 164(2), 385–419 http://dx.doi.org/10.1007/BF02101707
  • [2] Bhosle U.N., Moduli of vector bundles in characteristic 2, Math. Nachr., 2003, 254/255, 11–26 http://dx.doi.org/10.1002/mana.200310049
  • [3] Biswas I., Hoffmann N., The line bundles on moduli stacks of principal bundles on a curve, Doc. Math., 2010, 15, 35–72
  • [4] Biswas I., Hoffmann N., Poincaré families of G-bundles on a curve, Math. Ann., 2012, 352(1), 133–154 http://dx.doi.org/10.1007/s00208-010-0628-x
  • [5] Drezet J.-M., Narasimhan M.S., Groupe de Picard des variétés de modules de fibrés semi-stable sur les courbes algébriques, Invent. Math., 1989, 97(1), 53–94 http://dx.doi.org/10.1007/BF01850655
  • [6] Faltings G., Stable G-bundles and projective connections, J. Algebraic Geom., 1993, 2(3), 507–568
  • [7] Faltings G., Algebraic loop groups and moduli spaces of bundles, J. Eur. Math. Soc. (JEMS), 2003, 5(1), 41–68 http://dx.doi.org/10.1007/s10097-002-0045-x
  • [8] Grothendieck A., Éléments de Géométrie Algébrique. III. Étude Cohomologique des Faisceaux Cohérents. I, II, Inst. Hautes Études Sci. Publ. Math., 11, 17, Presses Universitaires de France, Paris, 1961, 1963
  • [9] Hoffmann N., Moduli stacks of vector bundles on curves and the King-Schofield rationality proof, In: Cohomological and Geometric Approaches to Rationality Problems, Progr. Math., 282, Birkhäuser, Boston, 2010, 133–148 http://dx.doi.org/10.1007/978-0-8176-4934-0_5
  • [10] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, 2nd ed., Cambridge Math. Lib., Cambridge University Press, Cambridge, 2010 http://dx.doi.org/10.1017/CBO9780511711985
  • [11] Joshi K., Mehta V.B., On the Picard group of moduli spaces, preprint available at http://arxiv.org/abs/1005.3007
  • [12] Knudsen F.F., Mumford D., The projectivity of the moduli space of stable curves. I. Preliminaries on “det” and “Div”, Math. Scand., 1976, 39(1), 19–55
  • [13] Mumford D., Fogarty J., Kirwan F., Geometric Invariant Theory, 3rd ed., Ergeb. Math. Grenzgeb., 34, Springer, Berlin, 1994 http://dx.doi.org/10.1007/978-3-642-57916-5
  • [14] Narasimhan M.S., Ramanan S., Moduli of vector bundles on a compact Riemann surface, Ann. Math., 1969, 89, 14–51 http://dx.doi.org/10.2307/1970807
  • [15] Osserman B., The generalized Verschiebung map for curves of genus 2, Math. Ann., 2006, 336(4), 963–986 http://dx.doi.org/10.1007/s00208-006-0026-6
  • [16] Seshadri C.S., Fibrés Vectoriels sur les Courbes Algébriques, Astérisque, 96, Société Mathématique de France, Paris, 1982
  • [17] Seshadri C.S., Vector bundles on curves, In: Linear Algebraic Groups and their Representations, Los Angeles, March 25–28, 1992, Contemp. Math., 153, American Mathematical Society, Providence, 1993, 163–200 http://dx.doi.org/10.1090/conm/153/01312
  • [18] Venkata Balaji T.E., Mehta V.B., Singularities of moduli spaces of vector bundles over curves in characteristic 0 and p, Michigan Math. J., 2008, 57, 37–42 http://dx.doi.org/10.1307/mmj/1220879395
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0064-0
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.