2010/08/18 by Qihong Xie, Xie, Qihong
Mathematics · Social Sciences · #14E30 #14F17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Vietnamese History and Culture Studies #math.AG #msc:14E30 #msc:14F17
paper · pdf · doi:10.48550/arxiv.1008.3024
14 pages
openalex publication_date 2010/08/18 · arxiv created 2011/01/10 · arxiv updated 2011/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 W2(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 W2(k), which can be used to construct a large class of liftable smooth projective varieties.