Geometry & Topology
- Geom. Topol.
- Volume 18, Number 5 (2014), 2747-2821.
Gromov–Witten/pairs descendent correspondence for toric $3$–folds
We construct a fully equivariant correspondence between Gromov–Witten and stable pairs descendent theories for toric –folds . Our method uses geometric constraints on descendents, 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 (conjectured by MNOP). Using descendent methods, we establish the relative GW/Pairs correspondence for in several basic new log Calabi–Yau geometries. Among the consequences is a rationality constraint for non-equivariant descendent Gromov–Witten series for .
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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Mathematical Reviews number (MathSciNet)
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]
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