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

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

doi:10.1090/jams/978

Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface
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by Hans-Joachim Hein, Song Sun, Jeff Viaclovsky and Ruobing Zhang

J. Amer. Math. Soc. 35 (2022), 123-209

DOI: https://doi.org/10.1090/jams/978

Published electronically: June 25, 2021

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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 $K3$ surface to the interval, with regular fibers diffeomorphic to either $3$-tori or Heisenberg nilmanifolds.

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