Duke Mathematical Journal

Extremal Kähler metrics on projectivized vector bundles

Till Brönnle

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Abstract

We prove the existence of extremal, nonconstant–scalar curvature, Kähler metrics on certain unstable projectivized vector bundles P(E)M over a compact constant–scalar curvature Kähler manifold M with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles EM are assumed to split as a direct sum of stable subbundles E=E1Es all having different Mumford–Takemoto slope, for example, μ(E1)>>μ(Es).

Article information

Source
Duke Math. J., Volume 164, Number 2 (2015), 195-233.

Dates
First available in Project Euclid: 30 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1422627047

Digital Object Identifier
doi:10.1215/00127094-2860166

Mathematical Reviews number (MathSciNet)
MR3306554

Zentralblatt MATH identifier
1325.53095

Subjects
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Citation

Brönnle, Till. Extremal Kähler metrics on projectivized vector bundles. Duke Math. J. 164 (2015), no. 2, 195--233. doi:10.1215/00127094-2860166. https://projecteuclid.org/euclid.dmj/1422627047


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