The KSBA moduli space of stable log Calabi-Yau surfaces
Valery Alexeev, Hülya Argüz, Pierrick Bousseau
公開日: 2024/2/23
Abstract
We prove that every irreducible component of the coarse Koll\'ar-Shepherd-Barron and Alexeev (KSBA) moduli space of stable log Calabi--Yau surfaces admits a finite cover by a projective toric variety. This verifies a conjecture of Hacking-Keel-Yu. The proof combines tools from log smooth deformation theory, the minimal model program, punctured log Gromov-Witten theory and mirror symmetry.