Period Integrals and Tautological Systems

TL;DR

This paper develops a framework for understanding period integrals of Calabi-Yau hypersurfaces and complete intersections in flag varieties through tautological systems of differential equations, connecting geometry and representation theory.

Contribution

It introduces the concept of tautological systems, providing explicit generators for differential equations governing period integrals in complex geometric settings.

Findings

Constructed holonomic systems for CY hypersurfaces

Generalized systems to CY complete intersections

Linked differential systems with representation theory

Abstract

We study period integrals of CY hypersurfaces in a partial flag variety. We construct a holonomic system of differential equations which govern the period integrals. By means of representation theory, a set of generators of the system can be described explicitly. The results are also generalized to CY complete intersections. The construction of these new systems of differential equations have lead us to the notion of a tautological system.