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The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

Published online by Cambridge University Press:  01 November 2012

Indranil Biswas ,
Ajneet Dhillon  and
Nicole Lemire
Indranil Biswas
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, Indiaindranil@math.tifr.res.in
Ajneet Dhillon
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canadaadhill3@uwo.ca
Nicole Lemire
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canadanlemire@uwo.ca
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Abstract

We find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

Keywords

Essential dimensionmoduli stackgerbetwisted sheafparabolic bundle
Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 3 , December 2012 , pp. 455 - 488
Copyright
Copyright © ISOPP 2012

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