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# Benoit Charbonneau : Asymptotic Hodge Theory of Vector Bundles

In joint work with Mark Stern, 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.

**Category**: Geometry and Topology**Duration**: 01:34:53**Date**: March 5, 2013 at 4:25 PM**Views**: 122-
**Tags:**seminar, Geometry/topology Seminar

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