Gromov-Witten Theory of P^1xP^1xP^1
Algebraic Geometry
2017-01-20 v3
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.
Keywords
Cite
@article{arxiv.1201.4414,
title = {Gromov-Witten Theory of P^1xP^1xP^1},
author = {Dagan Karp and Dhruv Ranganathan},
journal= {arXiv preprint arXiv:1201.4414},
year = {2017}
}
Comments
v3: 9 pages. Introduction has been rewritten. Several expository improvements throughout. To appear in Journal of Pure and Applied Algebra