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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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 HTML | PDF
J. Amer. Math. Soc. 35 (2022), 123-209 Request permission

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.
References
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Additional Information
  • Hans-Joachim Hein
  • Affiliation: Department of Mathematics, Fordham University, Bronx, New York 10458; and Mathematisches Institut, WWU Münster, 48149 Münster, Germany
  • MR Author ID: 938594
  • ORCID: 0000-0002-3719-9549
  • Email: hhein@uni-muenster.de
  • Song Sun
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 879901
  • Email: sosun@berkeley.edu
  • Jeff Viaclovsky
  • Affiliation: Department of Mathematics, University of California, Irvine, California 92697
  • MR Author ID: 648525
  • Email: jviaclov@uci.edu
  • Ruobing Zhang
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 1181360
  • Email: ruobingz@princeton.edu
  • Received by editor(s): July 24, 2018
  • Received by editor(s) in revised form: June 5, 2020, January 15, 2021, and January 30, 2021
  • Published electronically: June 25, 2021
  • Additional Notes: The first author was partially supported by NSF Grant DMS-1745517. The second author was supported by NSF Grant DMS-1708420, an Alfred P. Sloan Fellowship, and a grant from the Simons Foundation ($\sharp$488633, S.S.). The third author was partially supported by NSF Grant DMS-1811096. The fourth author was partially supported by NSF Grant DMS-1906265.
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 35 (2022), 123-209
  • MSC (2020): Primary 53C25, 53C26, 53C55
  • DOI: https://doi.org/10.1090/jams/978
  • MathSciNet review: 4322391