Intersection Numbers from Higher-order Partial Differential Equations

TL;DR

This paper introduces a novel method to evaluate intersection numbers of twisted meromorphic forms using higher-order PDEs and multivariate residues, demonstrated through examples in mathematics and physics.

Contribution

It presents a new approach combining PDE solutions and residue evaluation for intersection numbers, expanding computational tools in geometry and physics.

Findings

Effective evaluation of intersection numbers demonstrated

Method applied successfully to mathematical and physical examples

Provides algebraic expressions for residue contributions

Abstract

We propose a new method for the evaluation of intersection numbers for twisted meromorphic $n$-forms, through Stokes' theorem in $n$ dimensions. It is based on the solution of an $n$-th order partial differential equation and on the evaluation of multivariate residues. We also present an algebraic expression for the contribution from each multivariate residue. We illustrate our approach with a number of simple examples from mathematics and physics.