On the existence of Kähler metrics of constant scalar curvature

Kenji Tsuboi

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arXiv · 0902.0861

On the existence of Kähler metrics of constant scalar curvature

Kenji Tsuboi

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Abstract

For certain compact complex Fano manifolds $M$ with reductive Lie algebras of holomorphic vector fields, we determine the analytic subvariety of the second cohomology group of $M$ consisting of Kähler classes whose Bando-Calabi-Futaki character vanishes. Then a Kähler class contains a Kähler metric of constant scalar curvature if and only if the Kähler class is contained in the analytic subvariety. On examination of the analytic subvariety, it is shown that $M$ admits infinitely many nonhomothetic Kähler classes containing Kähler metrics of constant scalar curvature but does not admit any Kähler-Einstein metric.

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Kenji Tsuboi. 2009-02-05. On the existence of Kähler metrics of constant scalar curvature. https://arxiv.org/abs/0902.0861

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