Descendant and Fourier-Mukai equivalences for simple flops

TL;DR

This paper establishes a correspondence between genus 0 descendant Gromov-Witten theories of simple flops and demonstrates compatibility with Fourier-Mukai equivalences.

Contribution

It constructs a new link between descendant Gromov-Witten theories and Fourier-Mukai equivalences for simple flops.

Findings

Genus 0 descendant Gromov-Witten theories are related across simple flops.

Fourier-Mukai equivalences are compatible with these descendant correspondences.

Abstract

For a simple flop $X\dashrightarrow X'$, we construct a correspondence between genus $0$ descendant Gromov-Witten theories of $X$ and $X'$. We show that the Fourier-Mukai equivalence induced by $X\dashrightarrow X'$ is compatible, in a precise sense, with the descendant correspondence.