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Special Kaehler metrics on holomorphic submersions

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If you have a question about this talk, please contact Dhruv Ranganathan.

Proper holomorphic submersions of Kähler manifolds can be thought of as both a generalisation of holomorphic vector bundles and as a way of studying the behaviour of Kähler manifolds in families, one of the main goals of moduli theory. We will consider fibrations whose fibres are K-semistable varieties and admit a K-polystable degeneration, and we will describe a conditions, called optimal symplectic connection condition, which represents a canonical choice of a relatively Kähler metric and a generalisation of the Hermite-Einstein condition on vector bundles.

This talk is part of the Algebraic Geometry Seminar series.

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