Good moduli spaces for boundary polarized Calabi-Yau surface pairs

Abstract

We construct projective asymptotically good moduli spaces parametrizing boundary polarized CY surface pairs, which are projective slc Calabi-Yau pairs $(X,D)$ such that $D$ is ample and $X$ has dimension two. The moduli space provides a wall crossing between certain KSBA and K-moduli spaces and is the ample model of the Hodge line bundle. In the case of K3 surfaces with a non-symplectic automorphism, the moduli space gives a modular interpretation for the Baily--Borel compactification.