Families of curves with Higgs field of arbitrarily large kernel

Abstract

In this note we consider the flat bundle U and the kernel K of the Higgs field naturally associated to any (polarized) variation of Hodge structures of weight 1. We study how strict the inclusion of U in K can be in the geometric case. More precisely, for any smooth projective curve C of genus g (at least 2) and any k (between 0 and g-1), we construct non-isotrivial deformations of C over a quasi-projecive base such that K has rank k and U has rank at most (g+1)/2.

arXiv commentConstruction of the covering in the proof of Theorem 1.1 updated. Referee's comments incorporated

References in corpus (3)

• On totally geodesic submanifolds in the Jacobian locus
• On the Oort conjecture for Shimura varieties of unitary and orthogonal types
• Fujita decomposition and Hodge loci

Cited by in corpus (5)

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• Holomorphic 1-forms on the moduli space of curves
• The slope of fibred surfaces: unitary rank and Clifford index
• General infinitesimal variations of Hodge structure of ample curves in surfaces
• Rigidity of modular morphisms via Fujita decomposition