Collapsing K3 Surfaces and Moduli Compactification
Algebraic Geometry
2018-05-07 v1 Differential Geometry
Abstract
This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to discuss their Gromov-Hausdorff limits along any sequences, which are even not necessarily "maximally degenerating". Our results also give a proof of Kontsevich-Soibelman [KS04, Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.
Cite
@article{arxiv.1805.01724,
title = {Collapsing K3 Surfaces and Moduli Compactification},
author = {Yuji Odaka and Yoshiki Oshima},
journal= {arXiv preprint arXiv:1805.01724},
year = {2018}
}
Comments
12 pages