Compactifications of moduli of elliptic K3 surfaces: stable pair and toroidal

Abstract

We describe two geometrically meaningful compactifications of the moduli space of elliptic K3 surfaces via stable slc pairs, for two different choices of a polarizing divisor, and show that their normalizations are two different toroidal compactifications of the moduli space, one for the ramification divisor and another for the rational curve divisor. In the course of the proof, we further develop the theory of integral affine spheres with 24 singularities. We also construct moduli of rational (generalized) elliptic stable slc surfaces of types ${\mathbf{A}}_{\mathbf{n}}$ ($n\ge 1$), ${\mathbf{C}}_{\mathbf{n}}$ ($n\ge 0$) and ${\mathbf{E}}_{\mathbf{n}}$ ($n\ge 0$).

45 pages, many figures. Final version

References in corpus (3)

• Triangulations of the sphere and degenerations of K3 surfaces
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Moduli of polarized Calabi-Yau pairs

Cited by in corpus (8)

• Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions
• Non-minimal Elliptic Threefolds at Infinite Distance II: Asymptotic Physics
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Compact moduli of K3 surfaces with a nonsymplectic automorphism
• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• On log minimality of weak K-moduli compactifications of Calabi-Yau varieties
• Periods of elliptic surfaces with $p_g=q=1$
• Normal Forms and Tyurin Degenerations of K3 Surfaces Polarised by a Rank 18 Lattice