On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
On the Noether-Lefschetz theorem and some remarks on codimension-two cycles
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关于Noether-Lefschetz定理及余维二圈的一些评论
DOI：
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发表时间：
1985
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影响因子：
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通讯作者：
J. Harris
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文献类型：
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作者：
P. Griffiths;J. Harris
这里，“广义模”是指p~3中d次曲面的空间Pn的子变元存在一个可数并V，使得Pie(S)=Z对S~p N_V成立。似乎没有人说过这个定理，但从来没有完全证明过它。相反，他基于构造1给出了一个似是而非的论证：设G是p3中n次亏格为9的n次曲线的Hilbert格式，L(Gr3(D)L-~ip N是p3中d次曲面的空间，Zc~t~.，~·关联对应S.，o，a=(C，S)：C z S}。
Here, "of general moduli" means that there is a countable union V of subvarieties of the space pN of surfaces of degree d in p3, such that the statement Pie(S) = Z holds for S ~ p N _ V. Noether, it would seem, stated this theorem but never completely proved it. Instead, he gave a plausibility argument, based on the following construction 1 : let ,~.g be the Hilbert scheme of curves of degree n and genus 9 in p3, l(gr3(d)l -~ IP N the space of surfaces of degree d in p3, and ZC~t~.,~• the incidence correspondence S. ,o ,a = ( (C, S) : C z S } .