Compact moduli of K3 surfaces
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 $R\in nL$ 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 DOI:
 10.48550/arXiv.2101.12186
 arXiv:
 arXiv:2101.12186
 Bibcode:
 2021arXiv210112186A
 Keywords:

 Mathematics  Algebraic Geometry;
 14D22;
 14J28
 EPrint:
 To appear in Annals of Math