Discriminants, dual varieties and toric geometry

Tuesday, May 15, 2007 - 1:15pm - 2:15pm
Lind 305
Sandra Di Rocco (Royal Institute of Technology (KTH))
Given an algebraic variety, embedded in projective space, the closure of all hyperplanes tangent at some non singular point is called the dual variety. A general embedding has dual variety of co-dimension one (in the dual projective space) and hence defined by an irreducible homogeneous polynomial, called the discriminant. The study of the exceptional embeddings, i.e. the ones having dual variety of lower dimension, is a very classical problem in algebraic geometry, still open for many classes of varieties. I will explain the problem and give the solution for the class of non singular toric varieties.