Back to Algebraic Geometry Seminar: Spring 2013
Algebraic Geometry Seminar
Date: Tuesday, Feb 5, 2013
Time: 3:30PM - 4:30PM
Location: LCB 215
Tommaso de Fernex
University of Utah
Title |
The Nash problem on families of arcs |
Abstract |
Hironaka’s theorem on resolution of singularities allows to study the geometry of a singular variety by associating to it a smooth birational model. A more intrinsic approach to study singularities was proposed by Nash. The idea is to look at the space of arcs (i.e. analytic germs of curves) passing through the singular points. This space decomposes into finitely many irreducible families, and carries much of the information encoded in a resolution. The Nash problem gives a precise formulation of how such families of arcs should relate to resolutions of singularities. In this talk I will give an overview of the history and solution of the problem. |
Algebraic Geometry