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arXiv · 1908.06421

On projective manifolds with pseudo-effective tangent bundle

Genki Hosono·Masataka Iwai·Shin-ichi Matsumura
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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 $X \to Y$ to a flat projective manifold $Y$ such that its general fiber is rationally connected. Moreover, by applying this structure theorem, we classify all the minimal surfaces with pseudo-effective tangent bundle and study general non-minimal surfaces, which provide examples of (possibly singular) positively curved tangent bundles.

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Genki Hosono, Masataka Iwai, Shin-ichi Matsumura. 2019-08-18. On projective manifolds with pseudo-effective tangent bundle. https://doi.org/10.1017/s1474748020000754

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