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Infinitesimal invariants of mixed Hodge structures

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arxiv 2406.17118 v1 pith:7VW2IRT5 submitted 2024-06-24 math.AG

Rodolfo Aguilar , Mark Green , Phillip Griffiths This is my paper · ORCID
classification math.AG
keywords invariantscasehodgeinfinitesimalmixedstructuresanticanonicalassociated
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abstract

We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and in more detail in the case when $X$ is a cubic threefold. In this last setting, we obtain a generic global Torelli theorem for pairs.

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  1. Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives

    math.AG 2025-07 conditional novelty 7.0 of 10

    For special Gushel-Mukai threefolds, the invariant part of the infinitesimal period map is injective, and the kernel of the full period map has dimension exactly three.

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