Powers of Linear FormsAlgebra & Discrete Mathematics
|Speaker:||Bernd Sturmfels, UC Berkeley, Mathematics|
|Start time:||Fri, Feb 20 2009, 2:10PM|
What is the dimension of the space of polynomials of a certain degree that are annihilated by certain powers of fixed vector fields? We obtain explicit formulas by computing sagbi bases of Cox-Nagata rings. They count the number of lattice points in certain polytopes derived from root systems. For del Pezzo surfaces, Cox-Nagata rings are presented by quadratic polynomials, and, for the blow-up of projective n-space at n+3 points, this involves a beautiful connection between the Verlinde formula and phylogenetic algebraic geometry. This is joint work with Zhiqiang Xu.