摘要翻译：
给出紧、复、代数簇的射影态射和区域上相对充足的线丛，证明了由线丛决定的Beilinson、Bernstein、Deligne和Gabber分解定理的分解同构的一个适当选择得到纯Hodge结构的同构。证明是基于与线丛相关的分解同构的一个新的上同调刻划。证明了关于交上同调中的交形式、从上同调到交上同调的自然映射、投影和Hodge圈以及交上同调中的诱导态射的一些推论。
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英文标题：
《Hodge-theoretic aspects of the Decomposition Theorem》
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作者：
Mark Andrea 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：
  Given a projective morphism of compact, complex, algebraic varieties and a relatively ample line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the decomposition isomorphism of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber, yields isomorphisms of pure Hodge structures. The proof is based on a new cohomological characterization of the decomposition isomorphism associated with the line bundle. We prove some corollaries concerning the intersection form in intersection cohomology, the natural map from cohomology to intersection cohomology, projectors and Hodge cycles, and induced morphisms in intersection cohomology.
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PDF链接：
https://arxiv.org/pdf/0710.2708