Mathematics > Algebraic Geometry
[Submitted on 28 Jan 2021 (v1), last revised 3 Apr 2023 (this version, v3)]
Title:Compact moduli of K3 surfaces
View PDFAbstract: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 $R\in |nL|$ on each polarized K3 surface $(X,L)\in F_{2d}$. 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.
Submission history
From: Valery Alexeev [view email][v1] Thu, 28 Jan 2021 18:48:19 UTC (226 KB)
[v2] Fri, 26 Feb 2021 15:24:48 UTC (147 KB)
[v3] Mon, 3 Apr 2023 15:25:10 UTC (67 KB)
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