Geometry & Topology

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

Rahul Pandharipande and Aaron Pixton

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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 XD 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

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

Received: 4 December 2012
Revised: 25 October 2013
Accepted: 24 December 2013
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]

Gromov–Witten stable pairs descendents


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.

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