Nilpotent structures and collapsing RICCI-FLAT metrics on the K3 surface

Hans Joachim Hein; Song Sun; Jeff Viaclovsky; Ruobing Zhang

doi:10.1090/JAMS/978

Nilpotent structures and collapsing RICCI-FLAT metrics on the K3 surface

Hans Joachim Hein, Song Sun, Jeff Viaclovsky, Ruobing Zhang

Mathematics

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

24 Scopus citations

Abstract

We exhibit families of Ricci-flat Kähler metrics on the K3 surface which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K⁢3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

Original language	English (US)
Pages (from-to)	123-209
Number of pages	87
Journal	Journal of the American Mathematical Society
Volume	35
Issue number	1
DOIs	https://doi.org/10.1090/JAMS/978
State	Published - 2022

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/JAMS/978

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title = "Nilpotent structures and collapsing RICCI-FLAT metrics on the K3 surface",

abstract = "We exhibit families of Ricci-flat K{\"a}hler metrics on the K3 surface which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K⁢3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.",

author = "Hein, {Hans Joachim} and Song Sun and Jeff Viaclovsky and Ruobing Zhang",

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AU - Hein, Hans Joachim

AU - Sun, Song

AU - Viaclovsky, Jeff

AU - Zhang, Ruobing

PY - 2022

Y1 - 2022

N2 - We exhibit families of Ricci-flat Kähler metrics on the K3 surface which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K⁢3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

AB - We exhibit families of Ricci-flat Kähler metrics on the K3 surface which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K⁢3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

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JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

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Nilpotent structures and collapsing RICCI-FLAT metrics on the K3 surface

Abstract

All Science Journal Classification (ASJC) codes

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