Geometry of the logarithmic Hodge moduli space (with an Appendix joint with Siqing Zhang)

Abstract

We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-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 etale 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.

arXiv comment38 pages. Accepted version of the article. Comments are welcome

References in corpus (5)

• Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I
• Moduli of Stable Parabolic Connections, Riemann-Hilbert correspondence and Geometry of Painlevé equation of type VI, Part I
• Kobayashi-Hitchin correspondence for tame harmonic bundles II
• A support theorem for the Hitchin fibration: the case of $S{L}_n$
• Duality and nearby cycles over general bases

Cited by in corpus (1)

• Moduli spaces of framed logarithmic and parabolic connections on a Riemann surface