Back to Algebraic Geometry Seminar: Fall 2010
Algebraic Geometry Seminar
Date: Tuesday, Aug 31, 2010
Time: 3:30PM - 4:30PM
Location: LCB 323
Tommaso de Fernex
University of Utah
Title |
The valuation space of an isolated normal singularity. |
Abstract |
The Zariski space of a normal variety X encodes all resolutions of X. In joint work with Charles Favre and Sebastien Boucksom, we study positivity properties of divisors on the Zariski space of a normal variety X. In the case X has an isolated singularity, we concurrently work on the full space of valuations of rank one centered at the singular point and study properties of various functions on it. The motivation of our work comes from an old paper of Wahl, where he defines a “characteristic number” of the surface singularity – an invariant that vanishes if and only if the singularity is log canonical. Our goal is to extend Wahl’s result to all dimensions. By working in full generality (especially, without assuming X to be Q-Gorenstein), we also obtain interesting applications to global geometry, and address questions of the following type: Which projective varieties admit polarized finite endomorphisms of degree > 1? Is the property of being log-Fano preserved by finite morphisms of projective varieties? |
Algebraic Geometry