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 + Show 2 more

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

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Journal: Journal of the American Mathematical Society	Publication Date: Jun 25, 2021
Citations: 15	License type: publisher-specific, author manuscript

Affiliation: Fordham University, University of California, Berkeley, University of California, Irvine, Princeton University

#Ricci-flat Metrics #K3 Surface + Show 8 more

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Abstract

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.

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