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.
© 2011 Advances in Theoretical and Mathematical Physics
D. Karp, D. Ranganathan, P. Riggins, U. Whitcher, Toric Symmetry of CP 3, Compositio Math, http://arXiv:1109.5157 [math.AG] (2011)