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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Gromov–Witten/pairs descendent correspondence for toric $3$–folds

Rahul Pandharipande and Aaron Pixton

Geometry & Topology 18 (2014) 2747–2821
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 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.

Keywords
Gromov–Witten, stable pairs, descendents
Mathematical Subject Classification 2010
Primary: 14N35
Secondary: 14H60
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
Authors
Rahul Pandharipande
Departement Mathematik
ETH Zürich
HG G 55
Rämistrasse 101
8092 Zürich
Switzerland
Aaron Pixton
Department of Mathematics
Harvard University
Cambridge, MA 02138
USA