On Certain Vanishing Identities For Gromov-Witten Invariants

TL;DR

This paper proves vanishing identities for Gromov-Witten invariants, confirming conjectures by Liu and Xu in cases with large summation range and low genus, and establishing stronger identities in certain cases.

Contribution

It provides proofs of Liu and Xu's conjectures for large summation ranges and low genus, and introduces stronger vanishing identities.

Findings

Proved conjectures for large summation range cases.

Confirmed conjectures in low genus cases.

Established stronger vanishing identities in certain scenarios.

Abstract

In this paper, we study some vanishing identities for Gromov-Witten invariants conjectured by K. Liu and H. Xu. We will prove these conjectures in the case that the summation range is large compare to genus. In fact, in such cases, we can obtain a vanishing identity which is stronger than their conjectures. Moreover we will also prove their conjectures in low genus cases.