ON PROJECTIVE MANIFOLDS with PSEUDO-EFFECTIVE TANGENT BUNDLE

Genki Hosono, Masataka Iwai, Shin Ichi Matsumura

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
JournalJournal of the Institute of Mathematics of Jussieu
DOIs
Publication statusAccepted/In press - 2021

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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