We show various properties of smooth projective D-affine varieties. In particular, any smooth projective D-affine variety is algebraically simply connected and its image under a fibration is D-affine. In characteristic zero such D-affine varieties are also uniruled. We also show that (apart from a few small characteristics) a smooth projective surface is D-affine if and only if it is isomorphic to either ${\mathbb P}^2$ or ${\mathbb P}^1\times {\mathbb P}^1$. In positive characteristic, a basic tool in the proof is a new generalization of Miyaoka's generic semipositivity theorem.

中文翻译：

---

关于光滑射影D-仿射变异

我们展示了平滑射影 D 仿射变体的各种性质。特别是，任何平滑的射影 D-仿射簇在代数上都是简单连通的，并且它在纤维化下的图像是 D-仿射。在特征零中，这种 D-仿射变种也不受控制。我们还表明（除了一些小特征）光滑的射影表面是 D 仿射的当且仅当它同构于 ${\mathbb P}^2$ 或 ${\mathbb P}^1\times { \mathbb P}^1$。在实证方面，证明中的一个基本工具是对宫冈的泛型半正定理的新推广。