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January 2020 Rational curves on compact Kähler manifolds
Junyan Cao, Andreas Höring
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J. Differential Geom. 114(1): 1-39 (January 2020). DOI: 10.4310/jdg/1577502017

Abstract

Mori’s theorem yields the existence of rational curves on projective manifolds such that the canonical bundle is not nef. In this paper we study compact Kähler manifolds such that the canonical bundle is pseudoeffective, but not nef. We present an inductive argument for the existence of rational curves that uses neither deformation theory nor reduction to positive characteristic. The main tool for this inductive strategy is a weak subadjunction formula for log-canonical centres associated to certain big cohomology classes.

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Junyan Cao. Andreas Höring. "Rational curves on compact Kähler manifolds." J. Differential Geom. 114 (1) 1 - 39, January 2020. https://doi.org/10.4310/jdg/1577502017

Information

Received: 7 January 2016; Published: January 2020
First available in Project Euclid: 28 December 2019

zbMATH: 07147342
MathSciNet: MR4047551
Digital Object Identifier: 10.4310/jdg/1577502017

Rights: Copyright © 2020 Lehigh University

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Vol.114 • No. 1 • January 2020
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