Some index formulae on the moduli space of stable parabolic vector bundles

Details Some index formulae on the moduli space of stable parabolic vector bundles Some index formulae on the moduli space of stable parabolic vector bundles

2008-12-11

arxiv.org/abs/0812.2223v1

Mathematics

Differential Geometry

37 pages, 2 figures

Scientific paper

We study natural families of d-bar 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 recent result of Takhtajan and Zograf.

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