Toric Symmetry of P^3 and Enumerative Geometry

11/02/2010 - 12:15pm
11/02/2010 - 1:10pm
Dhruv Ranganathan and Paul Riggins (Harvey Mudd College)

In this talk, we will discuss the combinatorics and enumerative geometry of P3 and its toric blowups. In particular, we will discuss our recent work in which we perform an exhaustive study of toric symmetries of blowups of P3 which induce nontrivial action on Chow. The polytopes associated to these toric varieties include the associahedron, permutohedron, cyclohedron, all graph associahedra, and others. The connection to enumerative geometry is illuminated via Gromov-Witten (GW) theory. If time permits, we will discuss the GW theoretic implications of our work, namely that we obtain new symmetries in the all genus GW theory of P3 and its blowups.

Millikan 208 (Pomona College)