Tommaso de Fernex : The Nash problem on families of arcs

Posted by , part of the Algebraic Geometry Seminar.

At

Sept. 5, 2012, 4 p.m.

In

SEO 427

Abstract

Nash was the first to observe that the space of arcs through the singularities of a complex variety has finitely many irreducible components, each of which is naturally associated to a divisorial valuation of the function field of the variety. Every valuation arising in this way is essential for the singularity, in the sense that its center in any resolution of singularities is an irreducible component over the singular locus. The Nash problem asks whether, conversely, every essential valuation corresponds to a component of the space of arcs through the singularities. In this talk I will give an overview of the history and solution of the problem.