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arXiv · 1111.0591

Asymptotic Hodge Theory of Vector Bundles

Benoit Charbonneau·Mark Stern
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Abstract

We introduce several families of filtrations on the space of vector bundles over a smooth projective variety. These filtrations are defined using the large k asymptotics of the kernel of the Dolbeault Dirac operator on a bundle twisted by the kth power of an ample line bundle. The filtrations measure the failure of the bundle to admit a holomorphic structure. We study compatibility under the Chern isomorphism of these filtrations with the Hodge filtration on cohomology.

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Benoit Charbonneau, Mark Stern. 2011-11-02. Asymptotic Hodge Theory of Vector Bundles. https://doi.org/10.4310/cag.2015.v23.n3.a4

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