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2014 | 12 | 8 | 1157-1163
Tytuł artykułu

Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
8
Strony
1157-1163
Opis fizyczny
Daty
wydano
2014-08-01
online
2014-05-08
Twórcy
autor
autor
Bibliografia
  • [1] Beauville A., Laszlo Y., Sorger C., The Picard group of the moduli of G-bundles on a curve, Compositio Math., 1998, 112(2), 183–216 http://dx.doi.org/10.1023/A:1000477122220
  • [2] Biswas I., Hoffmann N., A Torelli theorem for moduli spaces of principal bundles over a curve, Ann. Inst. Fourier (Grenoble), 2012, 62(1), 87–106 http://dx.doi.org/10.5802/aif.2700
  • [3] Biswas I., Hogadi A., Brauer group of moduli spaces of PGL(r)-bundles over a curve, Adv. Math., 2010, 225(5), 2317–2331 http://dx.doi.org/10.1016/j.aim.2010.04.020
  • [4] Biswas I., Hogadi A., Holla Y.I., The Brauer group of desingularization of moduli spaces of vector bundles over a curve, Cent. Eur. J. Math., 2012, 10(4), 1300–1305 http://dx.doi.org/10.2478/s11533-012-0071-1
  • [5] Biswas I., Poddar M., Chen-Ruan cohomology of some moduli spaces, II, Internat. J. Math., 2010, 21(4), 497–522 http://dx.doi.org/10.1142/S0129167X10006094
  • [6] Bogomolov F.A., Brauer groups of fields of invariants of algebraic groups, Math. USSR-Sb., 1990, 66(1), 285–299 http://dx.doi.org/10.1070/SM1990v066n01ABEH001173
  • [7] Hoffmann N., Rationality and Poincaré families for vector bundles with extra structure on a curve, Int. Math. Res. Not. IMRN, 2007, 3, #rnm010
  • [8] Kang M., Prokhorov Yu.G., Rationality of three-dimensional quotients by monomial actions, J. Algebra, 2010, 324(9), 2166–2197 http://dx.doi.org/10.1016/j.jalgebra.2010.07.037
  • [9] King A., Schofield A., Rationality of moduli of vector bundles on curves, Indag. Math. (N.S.), 1999, 10(4), 519–535 http://dx.doi.org/10.1016/S0019-3577(00)87905-7
  • [10] Laszlo Y., Linearization of group stack actions and the Picard group of the moduli of SLr/µs-bundles on a curve, Bull. Soc. Math. France, 1997, 125(4), 529–545
  • [11] Mumford D., Abelian Varieties, Tata Inst. Fund. Res. Studies in Math., 5, Oxford University Press, London, 1970
  • [12] 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
  • [13] Narasimhan M.S., Ramanan S., Generalised Prym varieties as fixed points, J. Indian Math. Soc., 1975, 39, 1–19
  • [14] Newstead P.E., Rationality of moduli spaces of stable bundles, Math. Ann., 1975, 215(3), 251–268 http://dx.doi.org/10.1007/BF01343893
  • [15] Nitsure N., Cohomology of desingularization of moduli space of vector bundles, Compositio Math., 1989, 69(3), 309–339
  • [16] Raghunathan M.S., Universal central extensions. Appendix to “Symmetries and quantization: structure of the state space”, Rev. Math. Phys., 1994, 6(2), 207–225 http://dx.doi.org/10.1142/S0129055X94000110
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-014-0403-4
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