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arXiv · 1812.05891

Families of curves with Higgs field of arbitrarily large kernel

Víctor González-Alonso·Sara Torelli
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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.

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Víctor González-Alonso, Sara Torelli. 2018-12-14. Families of curves with Higgs field of arbitrarily large kernel. https://doi.org/10.1112/blms.12437

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