Workshop
The infinite Euclidean Distance discriminant
- Emil Horobet
Abstract
In this talk, we study the infinite ED discriminant, the variety of data points with infinite critical points of the distance function from themselves to a given variety. We present many examples of varieties that have such a discriminant, and we show that this relates to instances of morphisms where we do not have the purity of the branch locus, we give sufficient conditions on the varieties to have a non-empty infinite discriminant and finally, we classify all such curves in arbitrary dimension and all surfaces in three-space which have a one-dimensional infinite discriminant, via the explicit construction of all such surfaces.