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 counterexampl...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.展开更多
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
文摘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.
