On the image of mrc fibrations of projective manifolds with semi-positive holomorphic sectional curvature

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Abstract

In this paper, we pose several conjectures on structures and images of maximal rationally connected fibrations of smooth projective varieties admitting semi-positive holomorphic sectional curvature. Toward these conjectures, we prove that the canonical bundle of images of such fibrations is not big. Our proof gives a generalization of Yang’s solution using RC positivity for Yau’s conjecture. As an application, we show that any compact Kähler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.

Original languageEnglish
Pages (from-to)1419-1439
Number of pages21
JournalPure and Applied Mathematics Quarterly
Volume16
Issue number5
DOIs
Publication statusPublished - 2020

Keywords

  • Abelian varieties
  • Holomorphic sectional curvatures
  • Maximal rationally connected fibrations
  • Minimal models
  • RC positivity
  • Ruled surfaces

ASJC Scopus subject areas

  • Mathematics(all)

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