Fibrations with Constant Scalar Curvature Kähler Metrics and the Cm-line Bundle
نویسنده
چکیده
Let π : X → B be a holomorphic submersion between compact Kähler manifolds of any dimensions, whose fibres and base have no non-zero holomorphic vector fields and whose fibres admit constant scalar curvature Kähler metrics. This article gives a sufficient topological condition for the existence of a constant scalar curvature Kähler metric on X. The condition involves the CM-line bundle—a certain natural line bundle on B—which is proved to be nef. Knowing this, the condition is then implied by c1(B) < 0. This provides infinitely many Kähler manifolds of constant scalar curvature in every dimension, each with Kähler class arbitrarily far from the canonical class.
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