The Infinitesimal Torelli Theorem for hypersurfaces in abelian varieties

Abstract

Given a compact Kähler manifold, the Infinitesimal Torelli problem asks whether the differential of the period map of a Kuranishi family is injective. Unlike the classical Torelli theorem for curves, there is a negative answer for example for hyperelliptic curves of genus greater than $2$. Nevertheless the Infinitesimal Torelli Theorem holds for many other classes of manifolds. We will prove it for smooth hypersurfaces in simple abelian varieties with sufficiently high self-intersection giving an effective bound on a result by Green in this particular case.

Cited by in corpus (1)

• M-regularity of $\mathbb{Q}$-twisted sheaves and its application to linear systems on abelian varieties