Hodge-theoretic aspects of the Decomposition Theorem
Hodge-theoretic aspects of the Decomposition Theorem
复制标题
分解定理的霍奇理论方面
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
L. Migliorini
中科院分区：
文献类型：
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作者：
M. A. Cataldo;L. Migliorini
在给定紧的、复的代数变异的一个射影态射和一个相对充裕的线束上，我们证明了在线束的支配下，对Beilinson、Bernstein、Deligne和Gabber的分解定理的分解同构的一个合适的选择，产生了纯Hodge结构的同构。这个证明是基于与线束相关的分解同构的一个新的上同调刻画。证明了交上同调中的交形式、交上同调到交上同调的自然映射、投影和Hodge环以及交上同调中的诱导态。
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.