Asymptotic Hodge Theory of Vector Bundles

Details Asymptotic Hodge Theory of Vector Bundles Asymptotic Hodge Theory of Vector Bundles

2011-11-02

arxiv.org/abs/1111.0591v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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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