English

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}
}