Hodge filtrations and the higher direct images of canonical sheaves
Hodge filtrations and the higher direct images of canonical sheaves
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霍奇过滤和规范滑轮的更高直接图像
DOI：
10.1007/bf01388799
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发表时间：
1986
影响因子：
3.1
通讯作者：
N. Nakayama
中科院分区：
文献类型：
--
作者：
N. Nakayama
设n：X~ S是C上非奇异代数簇之间具有连通纤维的真满射。设S有一个开子集SO，使得S\SO是一个只有法向交叉的除数，并且是光滑的，其中Xo=~-l（SO），Zo=~ Z] Xo. SO上的局部系统R/~ o，Cxo形成了Hodge结构的一个变体，其中i> 0，权值为i. Put Jg~：=（Rino，Cxo）|（gso和令F%;我们假定局部系统R ′ ~ 0，C50围绕S\SO的所有局部单值系统都是幂幺的.设o~ s'是~ o'到S在W意义下的典范扩张. [6]他证明了FP（~ fs '）'= j，FP（~ d）C~ si是，φ ′的子丛，其中j：So~ S是包含.我们将证明以下内容
Let n: X~ S be a proper surjective morphism with connected fibers between nonsingular algebraic varieties over C. Assume that there is an open subset S o of S such that S\S o is a divisor with only normal crossings and that 7to: Xo--, S o is smooth, where Xo=~-l (So) and) Zo=~ Z] X o. The local system R/~ o, Cxo on S o forms a variation of Hodge structures with weight i for each i> 0. Put Jg~:=(Rino, Cxo)|(gso and let F%;~) be the p-th Hodge filtration of~'r We oo 9 assume that all the local monodromies of the local systems R'~ o, Cso aroundS\S o are unipotent. Let o~ s' be the canonical extension of~ o'to S in the sense of W. Schmid [6], in which he proves that FP (~ fs')'.= j, FP (~ d) C~ si are subbundles of,~', where j: So~ S is the inclusion. We shall prove the following