2024/02/23 by Alexeev, Valery, Argüz, Hülya, Bousseau, Pierrick
#Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2402.15117
We prove that every irreducible component of the coarse Kollár-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.