Algebraic Geometry Seminar
Tommaso de Fernex
University of Utah
The Nash problem on families of arcs
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.
Wednesday September 5, 2012 at 4:00 PM in SEO 427