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Reider's theorem : ウィキペディア英語版
Reider's theorem
In algebraic geometry, Reider's theorem gives conditions for a line bundle on a projective surface to be very ample.
==Statement==
Suppose that ''L'' is a line bundle on a smooth projective surface with canonical bundle K. Then Reider's theorem states that if ''L'' is nef, ''L''2 ≥ 10, and two (possibly infinitely near) points ''x'' and ''y'' are not separated by ''L'' + ''K'' then there is effective divisor ''D'' containing ''x'' and ''y'' with ''D'' . ''L'' = 0, ''D''2 = −1 or −2, or ''D''.''L'' = 1, ''D''2 = 0 or −1, or ''D''.''L'' = 2, ''D''2 = 0.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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