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 Relative Articles Torelli theorem for the moduli space of parabolic Higgs bundles Theta functions on the moduli space of parabolic bundles Rationality of Moduli Spaces of Parabolic Bundles A variation formula for the determinant line bundle. Compact subspaces of moduli spaces of stable bundles over class VII surfaces Variation of moduli of parabolic Higgs bundles The first Chern form on moduli of parabolic bundles On the motives of moduli of parabolic chains and parabolic Higgs bundles Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme Some index formulae on the moduli space of stable parabolic vector bundles Canonical Generators for the Cohomology of Moduli of Parabolic Bundles on Curves More...
Mathematics  2010

# Determinant line bundle on moduli space of parabolic bundles

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Abstract:

In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it. The construction of the Hermitian structure was indirect: The parabolic determinant line bundle was identified with the pullback of the determinant line bundle on a moduli space of usual vector bundles over a covering curve. The Hermitian structure on the parabolic determinant bundle was taken to be the pullback of the Quillen metric on the determinant line bundle on the moduli space of usual vector bundles. Here a direct construction of the Hermitian structure is given. For that we need to establish a version of the correspondence between the stable parabolic bundles and the Hermitian--Einstein connections in the context of conical metrics. Also, a recently obtained parabolic analog of Faltings' criterion of semistability plays a crucial role.

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