The 3–fold vertex via stable pairs

Pandharipande, Rahul; Thomas, Richard P

doi:10.2140/gt.2009.13.1835

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The $3$–fold vertex via stable pairs

Rahul Pandharipande and Richard P Thomas

Geometry & Topology 13 (2009) 1835–1876

DOI: 10.2140/gt.2009.13.1835

Abstract

The theory of stable pairs in the derived category yields an enumerative geometry of curves in $3$ –folds. We evaluate the equivariant vertex for stable pairs on toric $3$ –folds in terms of weighted box counting. In the toric Calabi–Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities.

The equivariant vertex governs primary insertions in the theory of stable pairs for toric varieties. We consider also the descendent vertex and conjecture the complete rationality of the descendent theory for stable pairs.

Keywords

curve, threefold, Gromov–Witten, toric

Mathematical Subject Classification 2000

Primary: 14N35

Secondary: 14M25, 14D20, 14J30

References

Publication

Received: 3 June 2008

Accepted: 25 February 2009

Published: 24 March 2009

Proposed: Jim Bryan

Seconded: Lothar Goettsche, Frances Kirwan

Authors

Rahul Pandharipande
Department of Mathematics Princeton University Princeton, NJ 08544 USA

Richard P Thomas
Department of Mathematics Imperial College London SW7 2AZ UK

Volume 13, issue 4 (2009)