On Smooth Projective D-Affine Varieties

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 0 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 P2 or P1×P1⁠. In positive characteristic, a basic tool in the proof is a new generalization of Miyaoka’s generic semipositivity theorem.