Infinitesimal invariants of mixed Hodge structures

TL;DR

This paper introduces infinitesimal invariants for mixed Hodge structures, applies them to specific geometric pairs, and proves a global Torelli theorem for certain cases, advancing understanding of Hodge theory in algebraic geometry.

Contribution

It defines new invariants for mixed Hodge structures and establishes a global Torelli theorem for pairs involving cubic threefolds.

Findings

Invariants characterized for pairs (X,Y) with X Fano 3-fold and Y K3 surface

Explicit description of invariants for cubic threefolds

Proved a generic global Torelli theorem for these pairs

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.