Uniform diameter estimates for Kaehler metrics in big cohomology classes

Duc-Bao Nguyen; Duc-Viet Vu

Uniform diameter estimates for Kaehler metrics in big cohomology classes

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arxiv 2410.18532 v2 pith:OSFQJWUE submitted 2024-10-24 math.DG math.CVmath.MG

Uniform diameter estimates for Kaehler metrics in big cohomology classes

Duc-Bao Nguyen , Duc-Viet Vu This is my paper

classification math.DG math.CVmath.MG

keywords diameterkaehlermetricsclassescohomologyestimatesuniformcase

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We generalize previous diameter estimates and local non-vanishing of volumes for Kaehler metrics to the case of big cohomology classes. In our proof, among other things, we will prove a uniform diameter estimate for a family of smooth Kaehler metrics only involving an integrability condition. We also have to use fine stability properties of complex Monge-Ampere equations with prescribed singularities.

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