## Geometry & Topology

### Gromov–Witten/pairs descendent correspondence for toric $3$–folds

#### 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, $An$ 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 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 $P3$.

#### Article information

Source
Geom. Topol., Volume 18, Number 5 (2014), 2747-2821.

Dates
Revised: 25 October 2013
Accepted: 24 December 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732883

Digital Object Identifier
doi:10.2140/gt.2014.18.2747

Mathematical Reviews number (MathSciNet)
MR3285224

Zentralblatt MATH identifier
1342.14114

#### Citation

Pandharipande, Rahul; Pixton, Aaron. Gromov–Witten/pairs descendent correspondence for toric $3$–folds. Geom. Topol. 18 (2014), no. 5, 2747--2821. doi:10.2140/gt.2014.18.2747. https://projecteuclid.org/euclid.gt/1513732883

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