Asian Journal of Mathematics

Volume 22 (2018)

Number 2

Special issue in honor of Ngaiming Mok (1 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

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

Pages: 285 – 290

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

Author

Jean-Pierre Demailly (CNRS, Institut Fourier, Université Grenoble Alpes, Grenoble, France)

Abstract

The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost Kähler–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.

Keywords

Fano manifold, numerically effective vector bundle, rational homogeneous manifold, Campana–Peternell conjecture, Kähler–Einstein metric, closed positive current, regularization of currents, Schauder fixed point theorem

2010 Mathematics Subject Classification

14J45, 14M17, 32C30, 32Q10, 32Q20

Full Text (PDF format)

Received 28 October 2017

Accepted 20 February 2018

Published 15 June 2018