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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Unstable polarized del Pezzo surfaces
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by Ivan Cheltsov and Jesus Martinez-Garcia PDF
Trans. Amer. Math. Soc. 372 (2019), 7255-7296 Request permission


We provide new examples of $K$-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide new obstructions for the existence of constant scalar curvature Kähler metrics on polarized smooth del Pezzo surfaces.
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Additional Information
  • Ivan Cheltsov
  • Affiliation: School of Mathematics, University of Edinburgh, Edinburgh, Scotland; and National Research University Higher School of Economics, Moscow, Russia
  • MR Author ID: 607648
  • Email:
  • Jesus Martinez-Garcia
  • Affiliation: Department of Mathematical Sciences, University of Bath, Bath, England
  • MR Author ID: 1073616
  • Email:
  • Received by editor(s): March 13, 2018
  • Received by editor(s) in revised form: February 21, 2019
  • Published electronically: August 5, 2019
  • Additional Notes: The first author was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project 5-100. This article was written while the authors were visiting the Max Planck Institute for Mathematics. We would like to thank the institute for the excellent working conditions.
    The second author was supported by the Simons Foundation under the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics (grant #488631, Johannes Nordström).
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7255-7296
  • MSC (2010): Primary 32Q20, 32Q26, 14J45, 14J26, 32Q15
  • DOI:
  • MathSciNet review: 4024553