UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 12, 2019

939 Evans Hall

3:45PM: Terminal singularities that are not Cohen-Macaulay

Burt Totaro

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.

5:00PM: Symmetric powers of algebraic and tropical curves

Madeline Brandt

In this talk I will give a description of the following recent result: the non-Archimedean skeleton of the d-th symmetric power of a smooth projective algebraic curve X is naturally isomorphic to the d-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X. In the talk I will give all necessary background definitions for understanding the above statement and I will sketch the proof.

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