Algebraic Geometry Seminar

A simplicity criterion for normal isolated singularities

Speaker: Tommaso de Fernex, University of Utah

Location: Warren Weaver Hall 317

Date: Tuesday, October 2, 2018, 3:30 p.m.


The link of an isolated singular point of a complex variety is an analytic invariant of the singularity. It is natural to ask how much information the link carries about the singularity; for instance, the link of a smooth point is a sphere, and one can ask whether the converse is true. Work of Mumford and Brieskorn has shown that this is the case for normal surface singularities but not in higher dimensions. Recently, McLean asked whether more structure on the link may provide a way to characterize smooth points, providing a positive answer in dimension three. In this talk, I will discuss how CR geometry can be used to define a link-theoretic invariant of singularities that distinguishes smooth points in all dimensions. The proof relies on a partial solution to the complex Plateau problem.