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摘要翻译：
给出了一个复代数簇X，定义了一个自然数，称为模维数，它度量了X的超越(co)同调的数量。当所有的(co)同调被代数圈跨越时，模维数精确地为零。本文的大部分内容是给出这个数字的估计，以及它很小的例子。作为一个应用，我们在许多例子中检验或重新检验了Hodge猜想：无约束四折叠、有理连通五折叠、由p_g=0的曲面组成的四折叠、p_g=0的曲面上少量点的Hilbert格式以及泛型超曲面。
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英文标题：
《Varieties with very little transcendental cohomology》
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作者：
Donu Arapura
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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 complex algebraic variety X, we define a natural number called the motivic dimension which measures the amount of transcendental (co)homology of X. It is zero precisely when all the (co)homolgy is spanned by algebraic cycles. Most of this paper is concerned with giving estimates on this number, along with examples where it is small. As an application, we check or recheck the Hodge conjectue in a number of examples: uniruled fourfolds, rationally connected fivefolds, fourfolds fibred by surfaces with p_g=0, Hilbert schemes of a small number points on surfaces with p_g=0, and generic hypersurfaces.
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PDF链接：
https://arxiv.org/pdf/0706.2506
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