Deformation Theory and Limiting Mixed Hodge Structures

TL;DR

This paper explores the relationship between deformation theory and limiting mixed Hodge structures, providing new insights into how degenerations of algebraic varieties influence their Hodge-theoretic properties.

Contribution

It introduces a novel framework connecting deformation theory with the structure of limiting mixed Hodge structures in degenerating families.

Findings

Established a correspondence between deformations and limiting mixed Hodge structures.

Provided criteria for the existence of certain limiting mixed Hodge structures.

Analyzed examples illustrating the theoretical results.

Abstract

This paper was motivated by the following question: Recall that for a smooth projective variety X whose polarized Hodge structure on H^n(X,Q)_{prim} leads to a period point ...