Uniqueness of optimal symplectic connections
Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constantscalar curvature Kähler metric. When the fibres admit continuous automorphisms, a choice of fibrewise constant scalarcurvature Kähler metric is not unique. An optimal symplectic connection is a...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Cambridge University Press
2021-01-01
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Series: | Forum of Mathematics, Sigma |
Subjects: | |
Online Access: | https://www.cambridge.org/core/product/identifier/S2050509421000153/type/journal_article |
Summary: | Consider a holomorphic submersion between compact Kähler manifolds, such that each fibre admits a constantscalar curvature Kähler metric. When the fibres admit continuous automorphisms, a choice of fibrewise constant scalarcurvature Kähler metric is not unique. An optimal symplectic connection is a choice of fibrewise constant scalar curvature Kähler metric satisfying a geometric partial differential equation. The condition generalises the Hermite-Einstein condition for a holomorphic vector bundle through the induced fibrewise Fubini-Study metric on the associated projectivisation. |
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ISSN: | 2050-5094 |