Affiliation:
1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland
Abstract
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 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 ${{\mathbb{P}}}^2$ 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.
Publisher
Oxford University Press (OUP)
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