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arXiv · 1801.09081

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

Shin-ichi Matsumura
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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 K\"ahler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.

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BibTeXRIS

Shin-ichi Matsumura. 2018-01-27. On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature. https://doi.org/10.4310/pamq.2020.v16.n5.a3

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