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SOME INDEX FORMULAE ON THE MODULI SPACE OF STABLE PARABOLIC VECTOR BUNDLES

Part of: Partial differential equations on manifolds; differential operators Curves

Published online by Cambridge University Press:  28 February 2013

PIERRE ALBIN  and
FRÉDÉRIC ROCHON
PIERRE ALBIN
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, USA email palbin@illinois.edu
FRÉDÉRIC ROCHON*
Affiliation:
Department of Mathematics, Australian National University, Australia
*
✉frederic.rochon@anu.edu.au
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Abstract

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We study natural families of $\bar {\partial } $-operators on the moduli space of stable parabolic vector bundles. Applying a families index theorem for hyperbolic cusp operators from our previous work, we find formulae for the Chern characters of the associated index bundles. The contributions from the cusps are explicitly expressed in terms of the Chern characters of natural vector bundles related to the parabolic structure. We show that our result implies formulae for the Chern classes of the associated determinant bundles consistent with a result of Takhtajan and Zograf.

Keywords

parabolic bundlescuspsindex formula

MSC classification

Secondary: 58J20: Index theory and related fixed point theorems 58J52: Determinants and determinant bundles, analytic torsion 14H60: Vector bundles on curves and their moduli
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 94 , Issue 1 , February 2013 , pp. 1 - 37
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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