Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

6^th  of March 2024, 14:30-16:00, room “Dal Passo”

 

 

 

 

 

 

 

 

Embedded deformations of curves with maximal variation of Hodge structure

 

Víctor González Alonso
Leibniz Universität Hannover

 

 

 

 

 

 

 Given a family of complex (smooth projective) manifolds, one can measure its non-triviality by looking at how much the Hodge structures of the fibres change. This leads to the notion of maximal (infinitesimal) variation of Hodge structure (IVHS).

 

In the case of families of curves, results of Lee-Pirola and of myself with Torelli imply that a general deformation of any curve has maximal IVHS. This is however not so clear if one wants the deformation to keep some further structure, such as the gonality of the curve or an embedding into a given surface. For example, it was only recently proved by Favale and Pirola that every smooth plane curve admits a deformation as a plane curve with maximal IVHS, and the question remains open for deformations of curves inside any other surface.

 

In this talk I will present a joint work in progress with Sara Torelli extending this result to curves in P¹ x P¹, which turns out to be way more involved than the plane case.

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry