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

Abstract

top
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.

How to cite

top

Indranil 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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [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. [11] Mumford D., Abelian Varieties, Tata Inst. Fund. Res. Studies in Math., 5, Oxford University Press, London, 1970 Zbl0223.14022
  12. [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. [13] Narasimhan M.S., Ramanan S., Generalised Prym varieties as fixed points, J. Indian Math. Soc., 1975, 39, 1–19 Zbl0422.14018
  14. [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. [15] Nitsure N., Cohomology of desingularization of moduli space of vector bundles, Compositio Math., 1989, 69(3), 309–339 Zbl0702.14007
  16. [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 ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.