English

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