The perverse filtration for the Hitchin fibration is locally constant

2018/08/07 by de Cataldo, Mark Andrea A., Maulik, Davesh
#14 #14A10 #14A15 #14D #14F45 #14H60 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02235

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.

Related

• Perverse Leray filtration and specialization with applications to the\n Hitchin morphism
• Perversity equals weight for Painlevé spaces
• Hitchin fibrations, abelian surfaces, and the P=W conjecture
• The Hodge theory of character varieties
• The Hodge filtration on nonabelian cohomology