Geometry of the logarithmic Hodge moduli space

Author:

de Cataldo Mark Andrea1,Herrero Andres Fernandez2,Zhang Siqing3

Affiliation:

1. Department of Mathematics Stony Brook University New York USA

2. Department of Mathematics Columbia University New York USA

3. Department of Mathematics Stony Brook University Stony Brook New York USA

Abstract

AbstractWe show the smoothness over the affine line of the Hodge moduli space of logarithmic ‐connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base is a field, we also prove that the Hodge moduli space is geometrically integral. Along the way, we prove the same results for the corresponding moduli spaces of logarithmic Higgs bundles and of logarithmic connections. We use smoothness to derive specialization isomorphisms on the étale cohomology rings of these moduli spaces; this includes the special case when the base is of mixed characteristic. In the special case where the base is a separably closed field of positive characteristic, we show that these isomorphisms are filtered isomorphisms for the perverse filtrations associated with the corresponding Hitchin‐type morphisms.

Funder

National Science Foundation

Publisher

Wiley

Subject

General Mathematics

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