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1 June 2012 On blowing up extremal Kähler manifolds
Gábor Székelyhidi
Duke Math. J. 161(8): 1411-1453 (1 June 2012). DOI: 10.1215/00127094-1593308

Abstract

We show that the blowup of an extremal Kähler manifold at a relatively stable point in the sense of GIT admits an extremal metric in Kähler classes that make the exceptional divisor sufficiently small, extending a result of Arezzo, Pacard, and Singer. We also study the K-polystability of these blowups, sharpening a result of Stoppa in this case. As an application we show that the blowup of a Kähler–Einstein manifold at a point admits a constant scalar curvature Kähler metric in classes that make the exceptional divisor small, if it is K-polystable with respect to these classes.

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Gábor Székelyhidi. "On blowing up extremal Kähler manifolds." Duke Math. J. 161 (8) 1411 - 1453, 1 June 2012. https://doi.org/10.1215/00127094-1593308

Information

Published: 1 June 2012
First available in Project Euclid: 22 May 2012

zbMATH: 1259.58002
MathSciNet: MR2931272
Digital Object Identifier: 10.1215/00127094-1593308

Subjects:
Primary: 58E11
Secondary: 35J30

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 8 • 1 June 2012
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