2018/12/31 by Víctor González-Alonso, Sara Torelli
Mathematics · #math.AG #msc:14D06 #msc:14C30 #msc:32G20
paper · pdf · doi:10.1112/blms.12437
Construction of the covering in the proof of Theorem 1.1 updated. Referee's comments incorporated
arxiv created 2019/06/06 · arxiv updated 2020/12/09
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.