Holonomic Systems for Period Mappings

TL;DR

This paper constructs explicit tautological systems for each component of period mappings, advancing the understanding of how complex structures vary in algebraic families.

Contribution

It provides a new explicit construction of tautological systems associated with period mappings, linking algebraic geometry and differential equations.

Findings

Explicit tautological systems are constructed for each component of period mappings.

The approach clarifies the algebraic structure underlying period integrals.

This work bridges the gap between period mappings and tautological systems.

Abstract

Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [LSY,LY] to understand period integrals of algebraic manifolds. In this paper, we give an explicit construction of a tautological system for each component of a period mapping.