Algebraic models of local period maps and Yukawa algebras

TL;DR

This paper develops algebraic L-infinity models for local period maps of compact Kähler manifolds, linking deformation theory, Hodge structures, and Yukawa couplings to deepen understanding of complex geometric structures.

Contribution

It introduces new L-infinity algebra models for local period maps and connects deformation theory with Yukawa couplings within a unified algebraic framework.

Findings

L-infinity models for local period maps are constructed.

Deformations constrained by Hodge structure strata are analyzed.

Yukawa coupling is interpreted within deformation theory.

Abstract

We describe some L-infinity model for the local period map of a compact Kaehler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a byproduct we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.