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Transactions of the American Mathematical Society

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

 
 

 

Unstable polarized del Pezzo surfaces


Authors: Ivan Cheltsov and Jesus Martinez-Garcia
Journal: Trans. Amer. Math. Soc. 372 (2019), 7255-7296
MSC (2010): Primary 32Q20, 32Q26, 14J45, 14J26, 32Q15
DOI: https://doi.org/10.1090/tran/7900
Published electronically: August 5, 2019
MathSciNet review: 4024553
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Abstract: 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
Email: i.cheltsov@ed.ac.uk

Jesus Martinez-Garcia
Affiliation: Department of Mathematical Sciences, University of Bath, Bath, England
Email: J.Martinez.Garcia@bath.ac.uk

DOI: https://doi.org/10.1090/tran/7900
Keywords: $K$-stability, cscK metric, del Pezzo surface, slope stability, flop.
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).
Article copyright: © Copyright 2019 American Mathematical Society