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 Kähler surface with semi-positive holomorphic sectional curvature is rationally connected, or a complex torus, or a ruled surface over an elliptic curve.

中文翻译：

---

关于具有半正全同截面曲率的射流歧管的MRC纤维图像

在本文中，我们对允许半正全同性截面曲率的光滑射影品种的最大有理连接纤维的结构和图像提出了几个猜想。针对这些猜想，我们证明了这种纤维化的规范图像束并不大。我们的证明给出了使用Y的猜想的RC阳性的Yang解的一般化。作为一个应用，我们证明了具有半正全同截面曲率的任何紧致的Kähler曲面是合理连接的，或者是复杂的圆环，或者是椭圆曲线上的直纹曲面。