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arXiv · 2203.11127

Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds

Philipp Licht
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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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Philipp Licht. 2022-03-21. Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds. https://arxiv.org/abs/2203.11127

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