Toric Symmetry of CP^3
arXiv:1109.5157
Abstract
We exhaustively analyze the toric symmetries of CP^3 and its toric blowups. Our motivation is to study toric symmetry as a computational technique in Gromov-Witten theory and Donaldson-Thomas theory. We identify all nontrivial toric symmetries. The induced nontrivial isomorphisms lift and provide new symmetries at the level of Gromov-Witten Theory and Donaldson-Thomas Theory. The polytopes of the toric varieties in question include the permutohedron, the cyclohedron, the associahedron, and in fact all graph associahedra, among others.
20 pages, many figures. Comments welcome!