Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II

Details Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II

2010-08-18

arxiv.org/abs/1008.3024v2

Mathematics

Algebraic Geometry

14 pages

Scientific paper

A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W_2(k). In this paper, first we prove that smooth toric varieties are strongly liftable. As a corollary, we obtain the Kawamata-Viehweg vanishing theorem for smooth projective toric varieties. Second, we prove the Kawamata-Viehweg vanishing theorem for normal projective surfaces which are birational to a strongly liftable smooth projective surface. Finally, we deduce the cyclic cover trick over W_2(k), which can be used to construct a large class of liftable smooth projective varieties.

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