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Gromov–Witten/pairs
descendent correspondence for toric $3$–folds
Rahul Pandharipande and Aaron Pixton |
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Geometry & Topology 18 (2014) 2747–2821
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Abstract |
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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 . |
Keywords
Gromov–Witten, stable pairs, descendents
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Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14H60
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References |
Publication
Received: 4 December 2012
Revised: 25 October 2013
Accepted: 24 December 2013
Published: 1 December 2014
Proposed: Jim Bryan
Seconded: Lothar Goettsche, Richard Thomas
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Authors |
| Rahul Pandharipande | |
| Departement Mathematik ETH Zürich HG G 55 Rämistrasse 101 8092 Zürich Switzerland |
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| Aaron Pixton | |
| Department of Mathematics Harvard University Cambridge, MA 02138 USA |
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