Pure and Applied Mathematics Quarterly
Volume 16 (2020)
The perverse filtration for the Hitchin fibration is locally constant
Pages: 1444 – 1464
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.
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. . The second-named author is supported by NSF FRG grant DMS 1159265.
Received 9 October 2019
Accepted 30 January 2020
Published 17 February 2021