Commutative Algebra Seminar

Title

On the singular locus of Hankel determinants and some of their degenerations

Abstract

This is an investigation of the ideal theoretic invariants of the gradient ideal of the determinant of some structural matrices, such as primary components, multiplicity, reductions and free resolution, along with a detailed study of homaloidal behavior.

A homaloidal form is a homogeneous polynomial whose polar map is a birational transformation. This work was motivated by a question of Dolgachev regarding an upper bound for the degree of a homaloidal polynomial in terms of the dimension of the ring.