Abstract
We show that the K-moduli spaces of log Fano pairs (P1 × P1, cC), where C is a (4,4) curve and their wall crossings coincide with the VGIT quotients of (2,4), complete intersection curves in P3. This, together with recent results by Laza and O'Grady, implies that these K-moduli spaces form a natural interpolation between the GIT moduli space of (4,4) curves on P1 × P1 and the Baily-Borel compactification of moduli of quartic hyperelliptic K3 surfaces.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1251-1291 |
| Number of pages | 41 |
| Journal | Journal of the Institute of Mathematics of Jussieu |
| Volume | 22 |
| Issue number | 3 |
| DOIs | |
| State | Published - May 16 2023 |
Funding
We would like to thank David Jensen, Radu Laza, Zhiyuan Li, Xiaowei Wang, and Chenyang Xu for helpful discussions. We also thank the referee for many valuable suggestions. This material is based upon work supported by the National Science Foundation under Grant DMS-1440140 while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the spring 2019 semester. The authors were supported in part by the American Institute of Mathematics as part of the AIM SQuaREs program. The first author was partially supported by an NSF Postdoctoral Fellowship and NSF Grant DMS-2001408. The second author was partially supported by the Gamelin Endowed Postdoctoral Fellowship of the MSRI. The third author was partially supported by the Della Pietra Endowed Postdoctoral Fellowship of the MSRI and NSF Grant DMS-2001317.
Keywords
- K-moduli
- K3 surfaces
- moduli
- variation of GIT
ASJC Scopus subject areas
- General Mathematics