Variations of Mixed Hodge Structures for a Pair

Speaker：Zhenjian Wang (Hefei National Laboratory)

Time：2026-5-21 14:30

Location：Conference Room S308 at Experiment Building at Haiyun Campus

Abstract:

This talk is based on the paper "Infinitesimal Invariants of Mixed Hodge Structures" by R. Aguilar, M. Green, and Ph. Griffiths. We discuss the general framework of variations of mixed Hodge structures for a pair (X,Y), where X is a smooth complex projective manifold and Y is a smooth hypersurface in X. We define the infinitesimal invariant using the derivative of the period map. For a Fano–K3 pair, i.e., X a cubic threefold and Y a smooth anticanonical section of X, we associate a cubic form C to the pair and relate the infinitesimal invariant to C. We then examine the Torelli theorem using this cubic form and point out gaps in the proof of the generic Torelli theorem by Aguilar–Green–Griffiths. If time permits, we give new proofs of some results in their work.