# An algorithm of computing cohomology intersection number of hypergeometric integrals

## TL;DR

This paper demonstrates that the cohomology intersection number of a twisted Gauss-Manin connection is a rational function and applies this to derive new quadratic relations for period integrals of K3 surfaces.

## Contribution

It introduces a method to compute cohomology intersection numbers as rational functions and applies it to establish novel quadratic relations for K3 surface period integrals.

## Key findings

- Cohomology intersection number is a rational function.
- Derived new quadratic relations for K3 surface period integrals.
- Provided a computational approach for twisted Gauss-Manin connections.

## Abstract

We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function. As an application, we obtain a new quadratic relation associated to period integrals of a certain family of K3 surfaces.