Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Terminal singularities that are not Cohen-Macaulay

Seminar | February 12 | 3:45-4:45 p.m. | 939 Evans Hall

 Burt Totaro, UCLA

 Department of Mathematics

I will explain the notion of terminal singularities. This is the mildest class of singularities that appears in constructing minimal models of algebraic varieties. In characteristic zero, terminal singularities are automatically Cohen-Macaulay, and this is very useful for the minimal model program. I will present the first known terminal singularity of dimension 3 which is not Cohen-Macaulay; it has characteristic 2. The example is surprisingly easy to describe. Many open problems remain, as I will discuss.