Crepant resolution conjecture for $\mathbb{C}^5/\mathbb{Z}_5$

TL;DR

This paper investigates the relationship between Gromov-Witten invariants of local projective space and orbifold quotients, explicitly states the crepant resolution conjecture, and proves it for genera 2 and 3.

Contribution

It explicitly formulates the crepant resolution conjecture for $C^5/Z_5$ and proves it for specific genera, advancing understanding of Gromov-Witten invariants in this context.

Findings

Conjecture explicitly formulated for all genera.

Proved for genus 2 and 3.

Establishes a link between local $P^4$ and orbifold invariants.

Abstract

We study the relationship between Gromov-Witten invariants of local $\mathbb{P}^4$ and Gromov-witten invariants of $[\mathbb{C}^5/\mathbb{Z}_5]$ for all genera. We state the crepant resolution conjecture in explicit form and prove this conjecture for $g=2,3.$