Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 5

The perverse filtration for the Hitchin fibration is locally constant

Pages: 1444 – 1464

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n5.a4

Authors

Mark Andrea A. de Cataldo (Stony Brook University, New York, N.Y., U.S.A.)

Davesh Maulik (Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

We prove that the perverse Leray filtration for the Hitchin morphism is locally constant in families, thus providing some evidence towards the validity of the $P = W$ conjecture due to de Cataldo, Hausel and Migliorini in non Abelian Hodge theory.

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The first-named author, who is partially supported by N.S.F. D.M.S. Grant n. 1600515, would like to thank the Freiburg Research Institute for Advanced Studies for the perfect working conditions; the research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n. [609305]. The second-named author is supported by NSF FRG grant DMS 1159265.

Received 9 October 2019

Accepted 30 January 2020

Published 17 February 2021