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摘要翻译：
Green和Griffiths引入了一些与正规函数有关的奇点概念，特别是与中维本原Hodge类有关的奇点概念。本文利用分解定理的更基本的方面，定义了与本原中维上同调类相关的全局奇点和局部奇点，并利用相对Hard Lefschetz定理，证明了这些奇点检测了本原类的全局平凡性和局部平凡性。在最后一节中，我们将Hodge猜想与本原类的局部不消失联系起来，写出一个经典的归纳论证。
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英文标题：
《A remark on singularities of primitive cohomology classes》
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作者：
Mark Andrea A. de Cataldo and Luca Migliorini
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最新提交年份：
2007
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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：
Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle dimensional primitive Hodge classes. In this note, by using the more elementary aspects of the Decomposition Theorem, we define global and local singularities associated with primitive middle dimensional cohomology classes and by using the Relative Hard Lefschetz Theorem, we show that these singularities detect the global and local triviality of the primitive class. In a final section, we write-up a classical inductive argument relating the Hodge conjecture to the local non-vanishing of primitive classes.
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PDF链接：
https://arxiv.org/pdf/0711.1307
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