Some numerical results in complex differential geometry

Abstract

The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from Geometric Invariant Theory, and to the asymptotics of high powers of positive line bundles. In the core of the paper these ideas are illustrated by detailed numerical results for a particular K3 surface.

References in corpus (2)

• On the asymptotic expansion of Bergman kernel
• An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds, II

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