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arXiv · 2003.02410

Deformation for coupled Kähler-Einstein metrics

Satoshi Nakamura
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Abstract

The notion of coupled Kähler-Einstein metrics was introduced recently by Hultgren-WittNyström. In this paper we discuss deformation of a coupled Kähler-Einstein metrics on a Fano manifold. In particular we obtain a necessary and sufficient condition for a coupled Kähler-Einstein metric to be deformed to another coupled Kähler-Einstein metric for a Fano manifold admitting non-trivial holomorphic vector fields. In addition we also discuss deformation for a coupled Käher-Einstein metric on a Fano manifold when the complex structure varies.

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Satoshi Nakamura. 2020-03-16. Deformation for coupled Kähler-Einstein metrics. https://arxiv.org/abs/2003.02410

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