A characterization of counterexamples to the kodaira-ramanujam vanishing theorem on surfaces in positive characteristic

  • Qihong XieEmail author


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.


Characterization Counterexample Kodaira-Ramanujam vanishing 

2000 MR Subject Classification

14F17 14E30 


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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina

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