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

作者：Xie Qihong^*

来源：Chinese Annals of Mathematics Series B, 2011, 32(5): 741-748.

DOI：10.1007/s11401-011-0668-x

• Characterization
• Counterexample
• Kodaira-Ramanujam vanishing

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.

• 出版日期2011-9
• 单位复旦大学