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The Brauer group of moduli spaces of vector bundles over a real curve


Authors: Indranil Biswas, Norbert Hoffmann, Amit Hogadi and Alexander H. W. Schmitt
Journal: Proc. Amer. Math. Soc. 139 (2011), 4173-4179
MSC (2010): Primary 14F22, 14D20, 14P99
DOI: https://doi.org/10.1090/S0002-9939-2011-10837-2
Published electronically: April 5, 2011
MathSciNet review: 2823062
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Abstract: Let $ X$ be a geometrically connected smooth projective curve of genus $ g_X \geq 2$ over $ \mathbb{R}$. Let $ M(r, \xi)$ be the coarse moduli space of geometrically stable vector bundles $ E$ over $ X$ of rank $ r$ and determinant $ \xi$, where $ \xi$ is a real point of the Picard variety $ \underline{\mathrm{Pic}}^d( X)$. If $ g_X = r = 2$, then let $ d$ be odd. We compute the Brauer group of $ M(r,\xi)$.


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Additional Information

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

Norbert Hoffmann
Affiliation: Institut für Mathematik, Freie Universität, Arnimallee 3, 14195 Berlin, Germany
Email: norbert.hoffmann@fu-berlin.de

Amit Hogadi
Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
Email: amit@math.tifr.res.in

Alexander H. W. Schmitt
Affiliation: Institut für Mathematik, Freie Universität, Arnimallee 3, 14195 Berlin, Germany
Email: alexander.schmitt@fu-berlin.de

DOI: https://doi.org/10.1090/S0002-9939-2011-10837-2
Keywords: Brauer group, moduli space, real algebraic curve
Received by editor(s): August 19, 2010
Received by editor(s) in revised form: October 13, 2010
Published electronically: April 5, 2011
Communicated by: Lev Borisov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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