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arXiv · 1201.4414

Gromov-Witten Theory of P^1xP^1xP^1

Dagan Karp·Dhruv Ranganathan
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Abstract

We use elementary geometric techniques to exhibit an explicit equivalence between certain sectors of the Gromov-Witten theories of blowups of P^1xP^1xP^1 and P^3. In particular, we prove that the all genus, virtual dimension zero Gromov-Witten theory of the blowup of P^3 at points coincides with that of the blowup at points of P^1xP^1xP^1, for non-exceptional classes. We observe a toric symmetry of the Gromov-Witten theory of P^1xP^1xP^1 analogous and intimately related to Cremona symmetry of P^3. Enumerative applications are given.

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Dagan Karp, Dhruv Ranganathan. 2012-01-21. Gromov-Witten Theory of P^1xP^1xP^1. https://arxiv.org/abs/1201.4414

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