Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface,Journal of the American Mathematical Society

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Nilpotent structures and collapsing Ricci-flat metrics on the K3 surface
Journal of the American Mathematical Society ( IF 3.5 ) Pub Date : 2021-06-25 , DOI: 10.1090/jams/978
Hans-Joachim Hein , Song Sun , Jeff Viaclovsky , Ruobing Zhang

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.

中文翻译：

K3 表面的幂零结构和塌陷 Ricci-flat 度量

摘要：我们在 K3 表面上展示了一系列 Ricci-flat Kähler 度量，它们坍塌到一个区间，Tian-Yau 和 Taub-NUT 度量以气泡的形式出现。从 $K3$ 表面到区间有一个相应的连续满射映射，规则纤维微分形为 $3$-tori 或 Heisenberg nilmanifolds。

更新日期：2021-06-25

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