Numerical Algorithms for Finding Balanced Metrics on Vector Bundles
Differential Geometry
2008-12-06 v2 Algebraic Geometry
Abstract
In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always converges to the balanced metric (\cite{S}). In \cite{DKLR}, 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.
Cite
@article{arxiv.0804.4005,
title = {Numerical Algorithms for Finding Balanced Metrics on Vector Bundles},
author = {Reza Seyyedali},
journal= {arXiv preprint arXiv:0804.4005},
year = {2008}
}