Gromov-Witten Theory of P^1\timesP^1\timesP^1

Details Gromov-Witten Theory of P^1\timesP^1\timesP^1 Gromov-Witten Theory of P^1\timesP^1\timesP^1

2012-01-21

arxiv.org/abs/1201.4414v1

Mathematics

Algebraic Geometry

12 pages. Comments welcome!

Scientific paper

We prove equivalences between the Gromov-Witten theories of four blowups of P1\timesP1\timesP1 and P3. In particular, we prove that the all genus, virtual dimension zero Gromov-Witten theory of the blowup of P3 at points precisely coincides with that of the blowup at points of P1 \times P1 \times P1, for non-exceptional classes. It follows that the all-genus stationary Gromov-Witten theory of P1 \times P1 \times P1 coincides with that of P3 in low degree. We also prove there exists a toric symmetry of the Gromov-Witten theory of P1\timesP1\timesP1 analogous to and intimately related to Cremona symmetry of P3. Enumerative applications are given.

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