## Duke Mathematical Journal

### Balanced metrics and Chow stability of projective bundles over Kähler manifolds

Reza Seyyedali

#### Abstract

In 1980, I. Morrison proved that the slope stability of a vector bundle of rank $2$ over a compact Riemann surface implies Chow stability of the projectivization of the bundle with respect to certain polarizations. Using the notion of balanced metrics and recent work of Donaldson, Zhang, Wang, and Phong-Sturm, we show that the statement holds for higher-rank vector bundles over compact algebraic manifolds of arbitrary dimension that admit constant scalar curvature metric and have discrete automorphism group

#### Article information

Source
Duke Math. J., Volume 153, Number 3 (2010), 573-605.

Dates
First available in Project Euclid: 4 June 2010

https://projecteuclid.org/euclid.dmj/1275671398

Digital Object Identifier
doi:10.1215/00127094-2010-032

Mathematical Reviews number (MathSciNet)
MR2667426

Zentralblatt MATH identifier
1204.32013

#### Citation

Seyyedali, Reza. Balanced metrics and Chow stability of projective bundles over Kähler manifolds. Duke Math. J. 153 (2010), no. 3, 573--605. doi:10.1215/00127094-2010-032. https://projecteuclid.org/euclid.dmj/1275671398

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