A Characterization of Counterexamples to the Kodaira-Ramanujam Vanishing Theorem on Surfaces in Positive Characteristic  

作　　者：Qihong XIE 

机构地区：[1]School of Mathematical Sciences, Fudan University, Shanghai 200433, China.

出　　处：《Chinese Annals of Mathematics,Series B》2011年第5期741-748,共8页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10901037);the Doctoral Program Foundation of the Ministry of Education of China (No. 20090071120004);the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry

摘　　要：The author gives a characterization of counterexamples to the Kodaira-Ramanujam vanishing theorem on smooth projective surfaces in positive characteristic.More precisely,it is reproved that if there is a counterexample to the Kodaira-Ramanujam vanishing theorem on a smooth projective surface X in positive characteristic,then X is either a quasi-elliptic surface of Kodaira dimension 1 or a surface of general type.Furthermore,it is proved that up to blow-ups,X admits a fibration to a smooth projective curve,such that each fiber is a singular curve.

关 键 词：CHARACTERIZATION COUNTEREXAMPLE Kodaira-Ramanujam vanishing 

分 类 号：O174.41[理学—数学] O484[理学—基础数学]