- CiteKey: “AET19” - Type: report - Title: “Stable pair compactification of moduli of K3 surfaces of degree 2,” - Author: “Alexeev, Valery; Engel, Philip; Thompson, Alan;” - Publisher: “arXiv,” - Year: 2019 - Collections: “Affine Dynkin Project,”
Stable pair compactification of moduli of K3 surfaces of degree 2
Meta
- URL: http://arxiv.org/abs/1903.09742
- URI: http://zotero.org/users/1049732/items/GJIX3X8T
- Open in Zotero: Zotero
Abstract
We prove that the universal family of polarized K3 surfaces of degree 2 can be extended to a flat family of stable slc pairs \((X,\epsilon R)\) over the toroidal compactification associated to the Coxeter fan. One-parameter degenerations of K3 surfaces in this family are described by integral-affine structures on a sphere with 24 singularities.
Extracted Annotations
Annotations(5/31/2022, 1:20:45 AM)
- Definition of moduli of polarized K3 Surfaces in terms of very ample divisor line bundles.
File:AET19_VZ57UFDN.png (Alexeev et al., 2019, p. 2)
- By Torelli it is a quasiprojective variety which is a global quotient. Discussion of the Baily-Borel compactification and toroidal compactifications in terms of an admissible fan. See effective divisor.
File:AET19_FM3GJTNA.png (Alexeev et al., 2019, p. 2)
- Discussion of the slc compactification in terms of stable pairs – pairs with slc singularities and very ample divisor log canonical class.
File:AET19_9K8TJVPT.png (Alexeev et al., 2019, p. 2)
- Motivating question: the boundary of BB and toroidal compactifications are easy to describe but not modular, while the slc compactification is modular but not easy to describe. Are there comparison maps?
File:AET19_YX3IW9IN.png (Alexeev et al., 2019, p. 2)
- Motivation from PPAVs, see Voronoi fan and theta divisor.
File:AET19_PLRBXLE3.png (Alexeev et al., 2019, p. 2)
- Main result, part 1. See K3 surface, toroidal compactification, admissible fan.
File:AET19_AMKHLRNT.png (Alexeev et al., 2019, p. 2)
- Main result, part 2. See Coxeter fan, semitoric compactification, stable pair compactification, Stein factorization, Normalization, and Dynkin diagrams.
File:AET19_EUPN7SL3.png (Alexeev et al., 2019, p. 3)
