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ON PROJECTIVE MANIFOLDS WITH PSEUDO-EFFECTIVE TANGENT BUNDLE

Part of: Surfaces and higher-dimensional varieties General theory of differentiable manifolds Compact analytic spaces

Published online by Cambridge University Press:  25 January 2021

Genki Hosono ,
Masataka Iwai Open the ORCID record for Masataka Iwai [Opens in a new window]  and
Shin-ichi Matsumura
Genki Hosono
Affiliation:
Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai980-8578, Japan (genki.hosono.a4@tohoku.ac.jp, genki.hosono@gmail.com)
Masataka Iwai
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan (masataka@ms.u-tokyo.ac.jp, masataka.math@gmail.com)
Shin-ichi Matsumura
Affiliation:
Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai980-8578, Japan (mshinichi-math@tohoku.ac.jp, mshinichi0@gmail.com)
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Abstract

In this paper, we develop the theory of singular Hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold X with pseudo-effective tangent bundle; X admits a smooth fibration $X \to Y$ to a flat projective manifold Y such that its general fibre is rationally connected. Moreover, by applying this structure theorem, we classify all the minimal surfaces with pseudo-effective tangent bundle and study general nonminimal surfaces, which provide examples of (possibly singular) positively curved tangent bundles.

Keywords

singular Hermitian metricspseudo-effective vector bundlestangent bundlesrationally connected varietiesabelian varietiesMRC fibrationsnumerically flat vector bundlessplitting of vector bundlesclassification of surfaces

MSC classification

Primary: 32J25: Transcendental methods of algebraic geometry
Secondary: 14J26: Rational and ruled surfaces 58A30: Vector distributions (subbundles of the tangent bundles)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1801 - 1830
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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