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

09/13/2011 - 12:15pm
09/13/2011 - 1:10pm
Dagan Karp (Harvey Mudd College)

I will report on work of Dhruv Ranganathan. We use toric symmetry and degeneration to study the GW theory of P1xP1xP1. The toric blowup of P1xP1xP1 at two points and six lines is isomorphic to the toric blowup of P3 at four points and six lines; this is the permutohedral variety. Just as permutohedral symmetry can be forced to descend to P3, we use degeneration to show permutohedral symmetry descends to P1xP1xP1. Thus P1xP1xP1 and P3 share the permutohedral symmetry. In this talk, I hope to give a friendly introduction to the central ideas in this project.

ML 134