Stationary Gromov-Witten invariants of projective spaces

TL;DR

This paper expresses stationary Gromov-Witten invariants of projective spaces as polynomials, analyzes their asymptotic behavior, and relates primary invariants to stationary descendants, providing new combinatorial and geometric insights.

Contribution

It introduces a polynomial representation of stationary Gromov-Witten invariants and links primary invariants to stationary descendants, enhancing understanding of their structure and asymptotics.

Findings

Stationary invariants are represented by explicit polynomials.

Asymptotic behavior relates to intersection numbers on moduli space.

Primary invariants are shown to be 'virtual' stationary descendants.

Abstract

We represent stationary descendant Gromov-Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of large degree behaviour of stationary descendant Gromov-Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov-Witten invariants are "virtual" stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants.