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

Details Brauer group of desingularization of moduli spaces of vector bundles over a curve Brauer group of desingularization of moduli spaces of vector bundles over a curve

2011-09-22

arxiv.org/abs/1109.4886v1

Mathematics

Algebraic Geometry

Scientific paper

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 and determinant L. We show that the Brauer group of any desingularization of M_C(r, L)$ is trivial. We also prove that the Brauer group of any desingularization of the moduli space of semistable principal PGL_r(k)-bundles on C is trivial.

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