## Duke Mathematical Journal

### Extremal Kähler metrics on projectivized vector bundles

Till Brönnle

#### Abstract

We prove the existence of extremal, nonconstant–scalar curvature, Kähler metrics on certain unstable projectivized vector bundles $\mathbb{P}(E)\to M$ over a compact constant–scalar curvature Kähler manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic Kähler classes. In particular, the vector bundles $E\to M$ are assumed to split as a direct sum of stable subbundles $E=E_{1}\oplus\cdots\oplus E_{s}$ all having different Mumford–Takemoto slope, for example, $\mu(E_{1})\gt \cdots\gt \mu(E_{s})$.

#### Article information

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

Dates
First available in Project Euclid: 30 January 2015

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

#### 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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