摘要翻译:
考虑拟射影流形U上G维阿贝尔簇F:a-->U。假定从U到极化阿贝尔簇模格式的诱导映射是泛型有限的,且存在射影流形Y,包含U作为一个法交因子S的补数,使得对数1形式的簇是nef并且它的行列式相对于U是充足的。我们用Hodge结构的变化所附的数值数据来刻画$U$是否是Shimura变体,而不是用从U到模格式的映射的性质或CM点的存在性来刻画。更确切地说,我们证明U是Shimura变体,当且仅当两个条件成立。首先,Hodge结构的复权一变分的每个不可约局部子系统V要么是酉的,要么满足Arakelov等式。其次,对于切丛为复球的U的泛覆盖中的每个因子M,与V相关的迭代Kodaira-Spencer映射在M方向上具有最小的可能长度。
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英文标题:
《Stability of Hodge bundles and a numerical characterization of Shimura
varieties》
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作者:
Martin Moeller, Eckart Viehweg, Kang Zuo
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最新提交年份:
2009
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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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一级分类:Mathematics 数学
二级分类:Complex Variables 复变数
分类描述:Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数,自守群作用与形式,伪凸性,复几何,解析空间,解析束
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英文摘要:
Consider a family f:A --> U of g-dimensional abelian varieties over a quasiprojective manifold U. Suppose that the induced map from U to the moduli scheme of polarized abelian varieties is generically finite and that there is a projective manifold Y, containing U as the complement of a normal crossing divisor S, such that the sheaf of logarithmic one forms is nef and that its determinant is ample with respect to U. We characterize whether $U$ is a Shimura variety by numerical data attached to the variation of Hodge structures, rather than by properties of the map from U to the moduli scheme or by the existence of CM points. More precisely, we show that U is a Shimura variety, if and only if two conditions hold. First, each irreducible local subsystem V of the complex weight one variation of Hodge structures is either unitary or satisfies the Arakelov equality. Secondly, for each factor M in the universal cover of U whose tangent bundle behaves like the one of a complex ball, an iterated Kodaira-Spencer map associated with V has minimal possible length in the direction of M.
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PDF链接:
https://arxiv.org/pdf/0706.3462