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Brauer group of a moduli space of parabolic vector bundles over a curve

Published online by Cambridge University Press:  18 February 2011

Indranil Biswas  and
Arijit Dey
Indranil Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India, indranil@math.tifr.res.in
Arijit Dey
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India, arijit@math.tifr.res.in
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Abstract

Let be a moduli space of stable parabolic vector bundles of rank n ≥ 2 and fixed determinant of degree d over a compact connected Riemann surface X of genus g(X) ≥ g(X) = 2, then we assume that n > 2. Let m denote the greatest common divisor of d, n and the dimensions of all the successive quotients of the quasi–parabolic filtrations. We prove that the Brauer group Br is isomorphic to the cyclic group ℤ/mℤ. We also show that Br is generated by the Brauer class of the Brauer–Severi variety over obtained by restricting the universal projective bundle over X × .

Keywords

Brauer groupparabolic bundlemoduli space

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 437 - 449
Copyright
Copyright © ISOPP 2011

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