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

Indranil Biswas; Amit Hogadi; Yogish Holla

Open Mathematics (2014)

- Volume: 12, Issue: 8, page 1157-1163
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topIndranil Biswas, Amit Hogadi, and Yogish Holla. "Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves." Open Mathematics 12.8 (2014): 1157-1163. <http://eudml.org/doc/269729>.

@article{IndranilBiswas2014,

abstract = {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.},

author = {Indranil Biswas, Amit Hogadi, Yogish Holla},

journal = {Open Mathematics},

keywords = {Semistable projective bundle; Moduli space; Rationality; Brauer group; Weil pairing; semistable projective bundle; moduli space; rationality},

language = {eng},

number = {8},

pages = {1157-1163},

title = {Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves},

url = {http://eudml.org/doc/269729},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Indranil Biswas

AU - Amit Hogadi

AU - Yogish Holla

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

JO - Open Mathematics

PY - 2014

VL - 12

IS - 8

SP - 1157

EP - 1163

AB - 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.

LA - eng

KW - Semistable projective bundle; Moduli space; Rationality; Brauer group; Weil pairing; semistable projective bundle; moduli space; rationality

UR - http://eudml.org/doc/269729

ER -

## References

top- [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 Zbl0976.14024
- [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 Zbl1268.14010
- [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 Zbl1211.14016
- [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 Zbl1281.14028
- [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 Zbl1189.14019
- [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 Zbl0759.14008
- [7] Hoffmann N., Rationality and Poincaré families for vector bundles with extra structure on a curve, Int. Math. Res. Not. IMRN, 2007, 3, #rnm010 Zbl1127.14031
- [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 Zbl1219.14017
- [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 Zbl1043.14502
- [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 Zbl0223.14022
- [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 Zbl0186.54902
- [13] Narasimhan M.S., Ramanan S., Generalised Prym varieties as fixed points, J. Indian Math. Soc., 1975, 39, 1–19 Zbl0422.14018
- [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 Zbl0288.14003
- [15] Nitsure N., Cohomology of desingularization of moduli space of vector bundles, Compositio Math., 1989, 69(3), 309–339 Zbl0702.14007
- [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 Zbl0841.20032

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.