Collapsing Ricci-flat metrics on elliptic K3 surfaces
Differential Geometry
2019-10-25 v1 Algebraic Geometry
Abstract
For any elliptic K3 surface , we construct a family of collapsing Ricci-flat K\"ahler metrics such that curvatures are uniformly bounded away from singular fibers, and which Gromov-Hausdorff limit to equipped with the McLean metric. There are well-known examples of this type of collapsing, but the key point of our construction is that we can additionally give a precise description of the metric degeneration near each type of singular fiber, without any restriction on the types of singular fibers.
Cite
@article{arxiv.1910.11321,
title = {Collapsing Ricci-flat metrics on elliptic K3 surfaces},
author = {Gao Chen and Jeff Viaclovsky and Ruobing Zhang},
journal= {arXiv preprint arXiv:1910.11321},
year = {2019}
}
Comments
77 pages