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

• Autorzy: Indranil Biswas , Amit Hogadi , Yogish Holla
• 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.

Słowa kluczowe

EN

Semistable projective bundle; Moduli space; Rationality; Brauer group; Weil pairing

Kategorie tematyczne

• 14E08: Rationality questions
• 14H60: Vector bundles on curves and their moduli
• 14F22: Brauer groups of schemes

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1157-1163

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

Indranil Biswas

• Tata Institute of Fundamental Research

autor

Amit Hogadi

• Tata Institute of Fundamental Research

autor

Yogish Holla

• Tata Institute of Fundamental Research

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

Identyfikatory

DOI

10.2478/s11533-014-0403-4