Back to Algebraic Geometry Seminar: Fall 2019
Algebraic Geometry Seminar
Date: Tuesday, Dec 3, 2019
Time: 3:30PM - 4:30PM
Location: LCB 222
Tommaso de Fernex
University of Utah
Title |
Measuring singularities of arc spaces |
Abstract |
The arc space of a variety is an infinite dimensional object. It relates to valuation theory, and has been used to define string theoretic invariants of singular Calabi-Yau varieties and to study singularities in the minimal model program. The infinitesimal structure of arc spaces present interesting features: the formal neighborhood of the arc space at k-rational arcs (where k is the ground field) is an infinite dimensional scheme, but a theorem of Drinfeld-Grinber-Kazhdan states that if the arc is not entirely contained in the singular locus of the variety then the singularities of the formal neighborhood are finite dimensional. The interest in this type of results originates from the expectation that there should be a well behaved theory of perverse sheaves on arc spaces. In this talk, I will present a novelle approach to these results which relies on a general notion of embedding codimension. The talk is based on joint work with Roi Docampo and Christopher Chiu. |
Algebraic Geometry