Back to Algebraic Geometry Seminar: Fall 2024
Algebraic Geometry Seminar
Date: Tuesday, Nov 19, 2024
Time: 3:30PM - 4:30PM
Location: LCB 222
Pierrick Bousseau
University of Georgia
Title |
The KSBA moduli space of stable log Calabi-Yau surfaces |
Abstract |
Abstract: The KSBA moduli space of stable pairs (X,B), introduced by Kollár–Shepherd-Barron, and Alexeev, is a natural generalization of the moduli space of stable curves for higher dimensional varieties. This moduli space is described concretely only in a handful of situations. For instance, if X is a toric variety and B=D+\epsilon C, where D is the toric boundary divisor and C is an ample divisor, it is shown by Alexeev that the KSBA moduli space is a toric variety. More generally, for stable pairs of the form (X,D+\epsilon C) with (X,D) a log Calabi-Yau variety and C an ample divisor, it was conjectured by Hacking–Keel–Yu that the KSBA moduli space is still toric (up to passing to a finite cover). In joint work with Alexeev and Arguz, we prove this conjecture for all log Calabi-Yau surfaces. This uses tools from the minimal model program, log smooth deformation theory and mirror symmetry. |
Algebraic Geometry