On Smooth Projective D-Affine Varieties
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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 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.
1991 ◽
Vol 122
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pp. 161-179
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1993 ◽
Vol 114
(3)
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pp. 461-470
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2001 ◽
Vol 130
(1)
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pp. 161-174
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1999 ◽
Vol 187
(1)
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pp. 187-199
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2001 ◽
Vol 64
(2)
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pp. 327-343
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2012 ◽
Vol 106
(2)
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pp. 225-286
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2018 ◽
Vol 70
(3)
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pp. 953-974
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