Three-dimensional algebraic manifolds having a divisor with a numerically trivial canonical class
Three-dimensional algebraic manifolds having a divisor with a numerically trivial canonical class
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具有数值平凡规范类除数的三维代数流形
DOI：
10.1070/rm1996v051n01abeh002752
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发表时间：
1996
影响因子：
0.9
通讯作者：
I Chel'tsov
中科院分区：
文献类型：
--
作者：
I Chel'tsov
H°(牛(D)®Οχ(-ηΗ))- > H°(牛(D)) - > H°(OY) +̂(ΟχΡ)®Οχ(-ηίΓ))。(2)Οχ(Β)反射性(见[2],1.6)和H”(牛{D)®Οχ(-ηίΓ))= 0 = 0,1,η> 0由引理1。由H°(OY) = C和(2)得到H°(OX(D)) = C，从而得到D ~ 0。定理。假设正常三维流形X具有丰富的有效Cartier因子Η，具有Du - Val奇点，且KJJ = 0。则-Κχ ~ Q Η， X是截面P （O H Φ QH(H\H)）的缩回，或者X具有正则奇点，Η是K3型曲面或Enriques曲面。
H°(OX(D) ® Οχ(-ηΗ)) —> H°(OX(D)) —> H°(OY) —+ ̂ ( Ο χ Ρ ) ® Οχ(-ηίΓ)). (2) Οχ(Β) is reflexive (see [2], 1.6) and H'(OX{D) ® Οχ(-ηίΓ)) = 0 for i = 0,1 and η > 0 by Lemma 1. From H°(OY) = C and from (2) we obtain H°(OX(D)) = C, and thus D ~ 0. Theorem. Suppose that the normal three-dimensional manifold X possesses an abundant effective Cartier divisor Η with Du Val singularities and KJJ = 0. Then —Κχ ~ Q Η and either X is a retraction of the section P ( O H Φ QH(H\H)) or X possesses canonical singularities and Η is a surface of type K3 or an Enriques surface.