Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface

Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface

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 \operatorname {K3} surface to the interval, with regular fibers diffeomorphic to eith...

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Veröffentlicht in:Journal of the American Mathematical Society 2022-01, Vol.35 (1), p.123-209
Hauptverfasser: Hein, Hans-Joachim, Sun, Song, Viaclovsky, Jeff, Zhang, Ruobing
Format: Artikel
Sprache:eng
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Research article
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Zusammenfassung: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 \operatorname {K3} surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.
ISSN:0894-0347
1088-6834
DOI:10.1090/jams/978