The KSBA moduli space of stable log Calabi-Yau surfaces
Algebraic Geometry
2025-09-25 v3 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2402.15117,
title = {The KSBA moduli space of stable log Calabi-Yau surfaces},
author = {Valery Alexeev and Hülya Argüz and Pierrick Bousseau},
journal= {arXiv preprint arXiv:2402.15117},
year = {2025}
}
Comments
93 pages, 10 figures. Final version accepted for publication in Forum of Mathematics, Pi