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 numerical dimension of images of such fibrations is zero under the assumption of the abundance 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.

53C25 (Primary), 32Q10, 14M22 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Jan 27

Keywords

  • Abelian varieties
  • Holomorphic sectional curvatures
  • Maximal rationally connected fibrations
  • Minimal models
  • Partially positive curvatures
  • Rationally connectedness
  • RC positivity
  • Ruled surfaces
  • Vanishing theorems

ASJC Scopus subject areas

  • General

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