The 3-fold vertex via stable pairs

Details The 3-fold vertex via stable pairs The 3-fold vertex via stable pairs

2007-09-24

arxiv.org/abs/0709.3823v2

Geometry & Topology 13, 1835-1876, 2009.

Mathematics

Algebraic Geometry

Typos fixed. 40 pages, 8 figures

Scientific paper

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.

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