論文

査読有り
2021年1月25日

ON PROJECTIVE MANIFOLDS WITH PSEUDO-EFFECTIVE TANGENT BUNDLE

Journal of the Institute of Mathematics of Jussieu
  • Genki Hosono
  • ,
  • Masataka Iwai
  • ,
  • Shin-Ichi Matsumura

開始ページ
1
終了ページ
30
記述言語
掲載種別
研究論文(学術雑誌)
DOI
10.1017/s1474748020000754
出版者・発行元
Cambridge University Press (CUP)

<title>Abstract</title>
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 <italic>X</italic> with pseudo-effective tangent bundle; <italic>X</italic> admits a smooth fibration <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S1474748020000754_inline1.png" />
<tex-math>$X \to Y$</tex-math>
</alternatives>
</inline-formula> to a flat projective manifold <italic>Y</italic> 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.

リンク情報
DOI
https://doi.org/10.1017/s1474748020000754
arXiv
http://arxiv.org/abs/arXiv:1908.06421
URL
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1474748020000754

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