ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE

Genki Hosono; Masataka Iwai; Shin Ichi Matsumura

doi:10.1017/S1474748020000754

ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE

Genki Hosono, Masataka Iwai, Shin Ichi Matsumura

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	1801-1830
Number of pages	30
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	21
Issue number	5
DOIs	https://doi.org/10.1017/S1474748020000754
Publication status	Published - 2022 Sept 25

Keywords

MRC fibrations
abelian varieties
classification of surfaces
numerically flat vector bundles
pseudo-effective vector bundles
rationally connected varieties
singular Hermitian metrics
splitting of vector bundles
tangent bundles

ASJC Scopus subject areas

Mathematics(all)

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10.1017/S1474748020000754

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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 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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T1 - ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE

AU - Hosono, Genki

AU - Iwai, Masataka

AU - Matsumura, Shin Ichi

N1 - Publisher Copyright: ©

PY - 2022/9/25

Y1 - 2022/9/25

N2 - 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 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.

AB - 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 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.

KW - MRC fibrations

KW - abelian varieties

KW - classification of surfaces

KW - numerically flat vector bundles

KW - pseudo-effective vector bundles

KW - rationally connected varieties

KW - singular Hermitian metrics

KW - splitting of vector bundles

KW - tangent bundles

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JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

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ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE

Abstract

Keywords

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