Gromov–Witten theory of P1×P1×P1

Authors

Dagan Karp, Harvey Mudd CollegeFollow
Dhruv Ranganathan, Yale University

Document Type

Article

Department

Harvey Mudd College, Mathematics (HMC)

Publication Date

Spring 2-4-2016

Abstract

We use elementary geometric techniques to exhibit an explicit equivalence between certain sectors of the Gromov–Witten theories of blowups of P¹×P¹×P¹P1×P1×P1 and P³P3. In particular, we prove that the all genus, virtual dimension zero Gromov–Witten theory of the blowup of P³P3 at points coincides with that of the blowup at points of P¹×P¹×P¹P1×P1×P1, for non-exceptional classes. We observe a toric symmetry of the Gromov–Witten theory of P¹×P¹×P¹P1×P1×P1 analogous and intimately related to Cremona symmetry of P³P3. Enumerative applications are given.

Recommended Citation

"Gromov-Witten Theory of P1xP1xP1"; Karp D., Ranganathan D. (2016); Journal of Pure and Applied Algebra. Volume 220, Issue 8, 2016, 3000-3009