Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles
Semi-algebraic chains on projective varieties and the Abel-Jacobi map for higher Chow cycles
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DOI：
10.1090/tran/8422
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发表时间：
2019-07
影响因子：
1.3
通讯作者：
Kenichiro Kimura
中科院分区：
文献类型：
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作者：
Kenichiro Kimura
我们将证明，相对于正则交叉除数的光滑准射影复变簇的奇异上同调群可以用 δ 容许链来描述。粗略地说，Delta 容许链是一条正确满足“面”的单纯半代数链。作为一个应用，我们证明了更高 Chow 循环的 Abel-Jacobi 图可以通过 delta 允许链来描述。作为一个例子，我们将根据 Abel-Jacobi 图描述 Bloch-Kriz 构建的多对数循环的 Hodge 实现。
We will show that the singular cohomology groups of a smooth quasi-projective complex variety relative to a normal crossing divisor can be described in terms of delta-admissible chains. Roughly speaking, a delta-admissible chain is a simplicial semi-algebraic chain meeting the "faces" properly. As an application, we show that the Abel-Jacobi map for higher Chow cycles can be described via delta-admissible chains. As an example, we will describe the Hodge realization of the polylog cycles constructed by Bloch-Kriz in terms of the Abel-Jacobi map.