Communications in Analysis and Geometry

Volume 23 (2015)

Number 3

Asymptotic Hodge theory of vector bundles

Pages: 559 – 609



Benoit Charbonneau (Department of Pure Mathematics, University of Waterloo, Ontario, Canada)

Mark Stern (Department of Mathematics, Duke University, Durham, North Carolina, U.S.A.)


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 $k$th 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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