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

By H. Hein, Song Sun, Jeff Viaclovsky, Ruobing Zhang. Journal of The American Mathematical Society, 2018

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We exhibit families of Ricci-flat Kahler metrics on K3 surfaces 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/71a656c12ddaedc399d0d05bffc01b0405f2596c