Asymptotic Hodge Theory of Vector Bundles
Differential Geometry
2015-02-04 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1111.0591,
title = {Asymptotic Hodge Theory of Vector Bundles},
author = {Benoit Charbonneau and Mark Stern},
journal= {arXiv preprint arXiv:1111.0591},
year = {2015}
}
Comments
23 pages