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

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 $g=2,3.$