ON PROJECTIVE MANIFOLDS WITH PSEUDO-EFFECTIVE TANGENT BUNDLE

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 r...

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Published inJournal of the Institute of Mathematics of Jussieu Vol. 21; no. 5; pp. 1801 - 1830
Main Authors Hosono, Genki, Iwai, Masataka, Matsumura, Shin-ichi
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2022
Subjects
Manifolds
Minimal surfaces
Theorems
14J26
singular Hermitian metrics
pseudo-effective vector bundles
splitting of vector bundles
tangent bundles
classification of surfaces
abelian varieties
32J25
MRC fibrations
numerically flat vector bundles
rationally connected varieties
58A30
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ISSN1474-7480
1475-3030
DOI10.1017/S1474748020000754

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Summary: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.
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content type line 14
ISSN:1474-7480
1475-3030
DOI:10.1017/S1474748020000754