Local behaviour of the kernel of the infinitesimal variation of Hodge structures of weight $1$ and applications

Sara Torelli

created by daniele on 11 Oct 2018
modified on 22 Nov 2018

29 nov 2018 -- 15:00

Aula Tricerri, DiMaI, Firenze

Abstract.

On the Hodge bundle of a any weight-$1$ polarized variation of Hodge structures over a curve one can define two nested vector subbundles: the flat bundle $U$ with the Gauss-Manin connection and the kernel bundle $K$ of the associated Higgs-field. By definition this last bundle describes the local behaviour of the infinitesimal variation and since $U \subset K$ one can ask if and how much their geometries can differ. In the seminar we present some algebraic and differential properties we have recently proven, highlighting how different phenomena can occur, and then we discuss about their applications (results and proposals) to the study of certain loci in the moduli of abelian varieties. This is intended to be a summary of the last two years of research.

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