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arXiv · 2402.15117

The KSBA moduli space of stable log Calabi-Yau surfaces

Valery Alexeev·Hülya Argüz·Pierrick Bousseau
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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.

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Valery Alexeev, Hülya Argüz, Pierrick Bousseau. 2024-02-23. The KSBA moduli space of stable log Calabi-Yau surfaces. https://arxiv.org/abs/2402.15117

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