Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds

2022/03/21 by Philipp Licht, Licht, Philipp
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2203.11127

Abstract

We generalize the classical approach of describing the infinitesimal Torelli map in terms of multiplication in a Jacobi ring to the case of quasi-smooth complete intersections in weighted projective space. As an application, we prove the infinitesimal Torelli theorem for hyperelliptic Fano threefolds of Picard rank 1, index 1, degree 4 and study the action of the automorphism group on cohomology. The results of this paper are used to prove Lang-Vojta's conjecture for the moduli of such Fano threefolds in a follow-up paper.

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