Algebraic Combinatorics Seminar - David Wagner

Title: Toric varieties from distributive lattices

Abstract:

Given a nite lattice L, consider the ring of complex polynomials in indeterminates indexed by L, modulo the ideal generated by (XaXb-Xa^bXa_b for all a; b 2 L). Hibi showed that this is an integral domain if and only if L is distributive, in which case the corresponding projective variety is toric. We describe the orbit decomposition and singularities of this variety in terms of the poset of join-irreducibles of L, and introduce a class of posets motivated by other questions about its geometry.