Asian Journal of Mathematics

Numerical Algorithm for Finding Balanced Metrics on Vector Bundles

Reza Seyyedali

Full-text: Open access

Abstract

In "Some numerical results in complex differential geometry," Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact Kähler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always converges to the balanced metric (Y. Sano, "Numerical algorithm for finding balanced metrics"). In "Numerical solution to the Hermitian Yang-Mills equation on the Fermat quintic," Douglas, et. al., conjecture that the same holds in the case of vector bundles. In this paper, we give an affirmative answer to their conjecture.

Article information

Source
Asian J. Math., Volume 13, Number 3 (2009), 311-322.

Dates
First available in Project Euclid: 24 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1261671490

Mathematical Reviews number (MathSciNet)
MR2570441

Zentralblatt MATH identifier
1183.53022

Subjects
Primary: 53C07: Special connections and metrics on vector bundles (Hermite-Einstein- Yang-Mills) [See also 32Q20]
Secondary: 32Q26: Notions of stability

Keywords
Holomorphic vector bundles Gieseker stability balanced metrics

Citation

Seyyedali, Reza. Numerical Algorithm for Finding Balanced Metrics on Vector Bundles. Asian J. Math. 13 (2009), no. 3, 311--322. https://projecteuclid.org/euclid.ajm/1261671490


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