摘要翻译：
正如B.Totaro所指出的那样，R.Thomas本质上证明了Hodge猜想归纳等价于称为广义Thomas超平面截面的超平面截面的存在，使得给定的本原Hodge类对它的限制不会消失。研究了一般光纤上同调中的消失圈之间的关系，证明了奇异超平面截面上的(0，0)型单幂单数消失圈之间的每一种关系都定义了一个本原Hodge类，使得这个奇异超平面截面是广义Thomas超平面截面当且仅当给定的本原Hodge类与某些构造的本原Hodge类之间的配对不消失。这是P.Griffiths对一个结构的概括。
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英文标题：
《Generalized Thomas hyperplane sections and relations between vanishing
  cycles》
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作者：
Morihiko Saito
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  As is remarked by B. Totaro, R. Thomas essentially proved that the Hodge conjecture is inductively equivalent to the existence of a hyperplane section, called a generalized Thomas hyperplane section, such that the restriction to it of a given primitive Hodge class does not vanish. We study the relations between the vanishing cycles in the cohomology of a general fiber, and show that each relation between the vanishing cycles of type (0,0) with unipotent monodromy around a singular hyperplane section defines a primitive Hodge class such that this singular hyperplane section is a generalized Thomas hyperplane section if and only if the pairing between a given primitive Hodge class and some of the constructed primitive Hodge classes does not vanish. This is a generalization of a construction by P. Griffiths.
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PDF链接：
https://arxiv.org/pdf/0806.1461