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

Pandharipande, Rahul¹ ; Pixton, Aaron²

¹ Departement Mathematik, ETH Zürich, HG G 55, Rämistrasse 101, 8092 Zürich, Switzerland
² Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Geometry & topology, Tome 18 (2014) no. 5, pp. 2747-2821.

Résumé

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, ${\mathcal{A}}_n$ 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 $P^3$.

Détail

DOI : 10.2140/gt.2014.18.2747

Classification : 14N35, 14H60
Keywords: Gromov–Witten, stable pairs, descendents

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