Back to Algebraic Geometry Seminar: Fall 2026
Algebraic Geometry Seminar
Date: Tuesday, Sep 1, 2026
Time: 3:30PM - 4:30PM
Location: LCB 215
Yuchen Liu
Northwestern University
Title |
Special valuations and automorphisms of affine log Calabi-Yau varieties |
Abstract |
The notion of special valuations, i.e. finitely generated valuations inducing klt degenerations of Fano varieties, plays an important role in the recent study of K-stability and moduli of Fano varieties. Given an affine log Calabi-Yau variety $U$, we show that its special skeleton, namely the space of special valuations in the dual complex of $U$, is independent of the choice of its Fano compactifications. Consequently, the special skeleton of $U$ is invariant under the action of $\text{Aut}(U)$. As an example, when $U$ is the complement of a Markov cubic surface in the affine three-space, we show that the action of three Vieta involutions on the special skeleton exhibits a surprising connection with dynamics on the hyperbolic plane. |
Algebraic Geometry