Note on equivariant $I$-function of local $P^n$

TL;DR

This paper extends previous results on hypergeometric series related to Gromov-Witten theory to an equivariant setting, aiding the study of higher genus Gromov-Witten invariants of Calabi-Yau geometries.

Contribution

It introduces an equivariant version of the $I$-function for local projective spaces, advancing the understanding of higher genus Gromov-Witten theories in this context.

Findings

Extended hypergeometric series properties to equivariant setting

Provided tools for higher genus Gromov-Witten computations

Enhanced understanding of Calabi-Yau geometries in Gromov-Witten theory

Abstract

Several properties of a hyepergeometric series related to Gromov-Witten theory of some Calabi-Yau geometries was studied in [8]. These properties play basic role in the study of higher genus Gromov-Witten theories. We extend the results of [8] to equivariant setting for the study of higher genus equivariant Gromov-Witten theories of some Calabi-Yau geometries.