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

Authors

Dagan Karp, Harvey Mudd CollegeFollow
Dhruv Ranganathan, Yale University

Document Type

Article

Department

Mathematics (HMC)

Publication Date

6-18-2012

Abstract

We prove equivalences between the Gromov-Witten theories of toric 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 precisely coincides with that of the blowup at points of P^1xP^1xP^1, for non-exceptional classes. It follows that the all-genus stationary Gromov-Witten theory of P^1xP^1xP^1 coincides with that of P^3 in low degree. We also prove there exists a toric symmetry of the Gromov-Witten theory of P^1xP^1xP^1 analogous to and intimately related to Cremona symmetry of P^3. Enumerative applications are given.

Rights Information

© 2012 Dagan Karp

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Recommended Citation

D. Karp, D. Ranganthan, Gromov-Witten Theory of P^1xP^1xP^1 http://arxiv.org/abs/1201.4414 (2012)