TY - JOUR
T1 - ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE
AU - Hosono, Genki
AU - Iwai, Masataka
AU - Matsumura, Shin Ichi
N1 - Publisher Copyright:
© The Author(s), 2021. Published by Cambridge University Press.
PY - 2021
Y1 - 2021
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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U2 - 10.1017/S1474748020000754
DO - 10.1017/S1474748020000754
M3 - Article
AN - SCOPUS:85100262000
JO - Journal of the Institute of Mathematics of Jussieu
JF - Journal of the Institute of Mathematics of Jussieu
SN - 1474-7480
ER -