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| A Characterization of Counterexamples to the Kodaira-Ramanujam Vanishing Theorem on Surfaces in Positive Characteristic |
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Citation： |
Qihong XIE.A Characterization of Counterexamples to the Kodaira-Ramanujam Vanishing Theorem on Surfaces in Positive Characteristic[J].Chinese Annals of Mathematics B,2011,32(5):741~748 |
| Page view： 1993
Net amount： 1567 |
Authors： |
Qihong XIE; |
Foundation： |
the National Natural Science Foundation of China (No. 10901037), the Doctoral
Program Foundation of the Ministry of Education of China (No. 20090071120004) and the Scientific
Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. |
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| Abstract： |
The author gives a characterization of counterexamples to the Kodaira-Ramanu-
jam vanishing theorem on smooth projective surfaces in positive characteristic. More pre-
cisely, 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 bration to a smooth projective curve, such
that each ber is a singular curve. |
Keywords： |
Characterization, Counterexample, Kodaira-Ramanujam vanishing |
Classification： |
14F17, 14E30 |
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