On smooth projective D-affine varieties

Abstract

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.

v2: 20 pages, to appear in Int. Math. Res. Not

References in corpus (1)

• Rank 3 rigid representations of projective fundamental groups