# The Brauer group of desingularization of moduli spaces of vector bundles over a curve

Indranil Biswas; Amit Hogadi; Yogish Holla

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1300-1305
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topIndranil Biswas, Amit Hogadi, and Yogish Holla. "The Brauer group of desingularization of moduli spaces of vector bundles over a curve." Open Mathematics 10.4 (2012): 1300-1305. <http://eudml.org/doc/269529>.

@article{IndranilBiswas2012,

abstract = {Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.},

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

journal = {Open Mathematics},

keywords = {Semistable bundle; Moduli space; Brauer group; semistable bundle; moduli space},

language = {eng},

number = {4},

pages = {1300-1305},

title = {The Brauer group of desingularization of moduli spaces of vector bundles over a curve},

url = {http://eudml.org/doc/269529},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Indranil Biswas

AU - Amit Hogadi

AU - Yogish Holla

TI - The Brauer group of desingularization of moduli spaces of vector bundles over a curve

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1300

EP - 1305

AB - Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.

LA - eng

KW - Semistable bundle; Moduli space; Brauer group; semistable bundle; moduli space

UR - http://eudml.org/doc/269529

ER -

## References

top- [1] Abramovich D., Corti A., Vistoli A., Twisted bundles and admissible covers, Comm. Algebra, 2003, 31(8), 3547–3618 http://dx.doi.org/10.1081/AGB-120022434 Zbl1077.14034
- [2] Balaji V., Cohomology of certain moduli spaces of vector bundles, Proc. Indian Acad. Sci. Math. Sci., 1988, 98(1), 1–24 http://dx.doi.org/10.1007/BF02880966 Zbl0687.14014
- [3] Balaji V., Biswas I., Gabber O., Nagaraj D.S., Brauer obstruction for a universal vector bundle, C. R. Math. Acad. Sci. Paris, 2007, 345(5), 265–268 http://dx.doi.org/10.1016/j.crma.2007.07.011 Zbl1127.14018
- [4] Gille P., Szamuely T., Central Simple Algebras and Galois Cohomology, Cambridge Stud. Adv. Math., 101, Cambridge University Press, Cambridge, 2006 http://dx.doi.org/10.1017/CBO9780511607219 Zbl1137.12001
- [5] Jarod A., Good Moduli Spaces for Artin Stacks, PhD thesis, Stanford University, 2008 Zbl1314.14095
- [6] 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
- [7] Laumon G., Moret-Bailly L., Champs Algébriques, Ergeb. Math. Grenzgeb., 39, Springer, Berlin, 2000
- [8] Narasimhan M.S., Ramanan S., Moduli of vector bundles on a compact Riemann surface, Ann. of Math., 1969, 89(1), 14–51 http://dx.doi.org/10.2307/1970807 Zbl0186.54902
- [9] Nitsure N., Cohomology of desingularization of moduli space of vector bundles, Compositio Math., 1989, 69(3), 309–339 Zbl0702.14007

## NotesEmbed ?

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