Duke Mathematical Journal

Extremal metrics on blowups

Claudio Arezzo, Frank Pacard, and Michael Singer

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Abstract

In this paper we provide conditions that are sufficient to guarantee the existence of extremal metrics on blowups at finitely many points of Kähler manifolds which already carry an extremal metric. As a particular case, we construct extremal metrics on P2 blown-up k points in general position, with k<m+2.

Article information

Source
Duke Math. J., Volume 157, Number 1 (2011), 1-51.

Dates
First available in Project Euclid: 16 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1300281532

Digital Object Identifier
doi:10.1215/00127094-2011-001

Mathematical Reviews number (MathSciNet)
MR2783927

Zentralblatt MATH identifier
1221.32008

Subjects
Primary: 32J27: Compact Kähler manifolds: generalizations, classification
Secondary: 32Q15: Kähler manifolds 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Citation

Arezzo, Claudio; Pacard, Frank; Singer, Michael. Extremal metrics on blowups. Duke Math. J. 157 (2011), no. 1, 1--51. doi:10.1215/00127094-2011-001. https://projecteuclid.org/euclid.dmj/1300281532


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