Fano manifolds with nef tangent bundles are weakly almost Kähler–Einstein

Jean-Pierre Demailly

Type: Article

Publication Date: 2018-01-01

Citations: 1

DOI: https://doi.org/10.4310/ajm.2018.v22.n2.a5

Abstract

The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost K{ä}hler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1, 1)-currents. We also discuss related semistability questions and Chern inequalities.

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