Collapsing Ricci-flat metrics on elliptic K3 surfaces

Gao Chen; Jeff Viaclovsky; Ruobing Zhang

doi:10.4310/CAG.2020.V28.N8.A9

Collapsing Ricci-flat metrics on elliptic K3 surfaces

Gao Chen, Jeff Viaclovsky, Ruobing Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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 language	English (US)
Pages (from-to)	2019-2133
Number of pages	115
Journal	Communications in Analysis and Geometry
Volume	28
Issue number	8
DOIs	https://doi.org/10.4310/CAG.2020.V28.N8.A9
State	Published - Jan 8 2021

All Science Journal Classification (ASJC) codes

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

Access to Document

10.4310/CAG.2020.V28.N8.A9

Cite this

@article{c4de95a0e9af4f62a1659e9f97474062,

title = "Collapsing Ricci-flat metrics on elliptic K3 surfaces",

abstract = "For any elliptic K3 surface F: K → P1, we construct a family of collapsing Ricci-flat K{\"a}hler 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.",

author = "Gao Chen and Jeff Viaclovsky and Ruobing Zhang",

year = "2021",

month = jan,

day = "8",

doi = "10.4310/CAG.2020.V28.N8.A9",

language = "English (US)",

volume = "28",

pages = "2019--2133",

journal = "Communications in Analysis and Geometry",

issn = "1019-8385",

publisher = "International Press of Boston, Inc.",

number = "8",

}

TY - JOUR

T1 - Collapsing Ricci-flat metrics on elliptic K3 surfaces

AU - Chen, Gao

AU - Viaclovsky, Jeff

AU - Zhang, Ruobing

PY - 2021/1/8

Y1 - 2021/1/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85099939214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099939214&partnerID=8YFLogxK

U2 - 10.4310/CAG.2020.V28.N8.A9

DO - 10.4310/CAG.2020.V28.N8.A9

M3 - Article

AN - SCOPUS:85099939214

SN - 1019-8385

VL - 28

SP - 2019

EP - 2133

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 8

ER -

Collapsing Ricci-flat metrics on elliptic K3 surfaces

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this