On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature
On the image of MRC fibrations of projective manifolds with semi-positive holomorphic sectional curvature
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DOI：
10.4310/pamq.2020.v16.n5.a3
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发表时间：
2018-01
影响因子：
0.7
通讯作者：
Shin-ichi Matsumura
中科院分区：
文献类型：
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作者：
Shin-ichi Matsumura
本文对具有半正全纯截面曲率的光滑射影簇的极大有理连通纤维化的结构和象作了一些讨论。对于这些结构，我们证明了在丰度猜想的假设下，这种纤维化的图像的数值维数为零。作为应用，我们证明了任何具有半正全纯截面曲率的紧致Kaehler曲面都是有理连通的，或者是复环面，或者是椭圆曲线上的直纹曲面。
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 Kaehler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.