Collapsing Ricci-flat metrics on elliptic K3 surfaces

Gao Chen, Jeff Viaclovsky, Ruobing Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

For any elliptic K3 surface F: K → P1, we construct a family of collapsing Ricci-flat Kähler metrics such that curvatures are uniformly bounded away from singular fibers, and which Gromov-Hausdorff limit to P1 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.

Original languageEnglish (US)
Pages (from-to)2019-2133
Number of pages115
JournalCommunications in Analysis and Geometry
Volume28
Issue number8
DOIs
StatePublished - Jan 8 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Collapsing Ricci-flat metrics on elliptic K3 surfaces'. Together they form a unique fingerprint.

Cite this