Virasoro Constraints of Curves as Residues

TL;DR

This paper reformulates Virasoro constraints for curves using residues of multilinear differentials, enabling computation of Gromov-Witten invariants' n-point functions, inspired by topological recursion methods.

Contribution

It introduces a novel residue-based formulation of Virasoro constraints for curves, connecting topological recursion with Gromov-Witten theory.

Findings

Residue formulation simplifies computation of Gromov-Witten invariants.

Provides a new perspective linking topological recursion and algebraic geometry.

Enables explicit calculation of n-point functions for curves.

Abstract

Inspired by Eynard-Orantin topological recursions, we reformulate the Virasoro constraints for curves as residues of multilinear differentials. As applications they can be used to compute the $n$-point functions of Gromov-Witten invariants of curves.