English

Collapsing Ricci-flat metrics on elliptic K3 surfaces

Differential Geometry 2019-10-25 v1 Algebraic Geometry

Abstract

For any elliptic K3 surface F:KP1\mathfrak{F}: \mathcal{K} \rightarrow \mathbb{P}^1, 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 P1\mathbb{P}^1 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.

Keywords

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

R2 v1 2026-06-23T11:54:07.281Z