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arXiv · 1906.00227

On smooth projective D-affine varieties

Adrian Langer
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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.

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Adrian Langer. 2019-06-01. On smooth projective D-affine varieties. https://doi.org/10.1093/imrn%2Frnz370

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