Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds
Algebraic Geometry
2022-07-13 v2
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.
Keywords
Cite
@article{arxiv.2203.11127,
title = {Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds},
author = {Philipp Licht},
journal= {arXiv preprint arXiv:2203.11127},
year = {2022}
}