On coupled constant scalar curvature Kähler metrics

Ved V. Datar; Vamsi Pritham Pingali

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arXiv · 1901.10454

On coupled constant scalar curvature Kähler metrics

Ved V. Datar·Vamsi Pritham Pingali

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Abstract

We provide a moment map interpretation for the coupled Kähler-Einstein equations introduced by Hultgren and Witt Nyström, and in the process introduce a more general system of equations, which we call coupled cscK equations. A differentio-geometric formulation of the corresponding Futaki invariant is obtained and a notion of K-polystability is defined for this new system. Finally, motivated by a result of Székelyhidi, we prove that if there is a solution to our equations, then small K-polystable perturbations of the underlying complex structure and polarizations also admit coupled cscK metrics.

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Ved V. Datar, Vamsi Pritham Pingali. 2019-02-26. On coupled constant scalar curvature Kähler metrics. https://arxiv.org/abs/1901.10454

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