Compact moduli of K3 surfaces

2021/01/28 by Alexeev, Valery, Engel, Philip · 3 citations
#14D22 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2101.12186

Abstract

We construct geometric compactifications of the moduli space F_2d of polarized K3 surfaces, in any degree 2d. Our construction is via KSBA theory, by considering canonical choices of divisor R∈ |nL| on each polarized K3 surface (X,L)∈ F_2d. The main new notion is that of a recognizable divisor R, a choice which can be consistently extended to all central fibers of Kulikov models. We prove that any choice of recognizable divisor leads to a semitoroidal compactification of the period space, at least up to normalization. Finally, we prove that the rational curve divisor is recognizable for all degrees.

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