Gromov-Witten/Pairs descendent correspondence for toric 3-folds

TL;DR

This paper establishes a comprehensive equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds, utilizing geometric constraints, the topological vertex, and rationality properties, with applications to non-equivariant limits and log Calabi-Yau geometries.

Contribution

It constructs the first fully equivariant descendent correspondence for toric 3-folds, proving its non-equivariant limit and applying it to various geometries and series.

Findings

Established a non-equivariant limit of the correspondence

Proved an explicit stationary descendent correspondence for toric 3-folds

Derived rationality constraints for Gromov-Witten series in P^3

Abstract

We construct a fully equivariant correspondence between Gromov-Witten and stable pairs descendent theories for toric 3-folds X. Our method uses geometric constraints on descendents, A_n surfaces, and the topological vertex. The rationality of the stable pairs descendent theory plays a crucial role in the definition of the correspondence. We prove our correspondence has a non-equivariant limit. As a result of the construction, we prove an explicit non-equivariant stationary descendent correspondence for X (conjectured previously by MNOP). Using descendent methods, we establish the relative GW/Pairs correspondence for X/D in several basic new log Calabi-Yau geometries. Among the consequences is a rationality constraint for non-equivariant descendent Gromov-Witten series for P^3.