Title: Infinitesimal VHS, and the peculiar case of genus 4 curves
Speaker: Matteo Verni (Paris Sorbonne)
Abstract: The infinitesimal Torelli theorem for curves states that for any non-hyperelliptic curve C, a small deformation of C is entirely determined by the induced deformation of the Hodge structure on H^1(C,Z). In other words, the local period mapping P has injective differential dP_C around any non-hyperelliptic curve C.
Can we say more about C by knowing the linear map dP_C ? For the general curve C of genus at least 5, dP_C contains the data of the equations cutting out the canonically embedded curve C inside projective (g-1)-space, while for genus 4… not quite. In this talk we explain how Griffiths’ theory of infinitesimal invariants allows us to recover a canonically embedded genus 4 curve from its small deformations.
Some snacks will be provided before and after the talk.