We answer two questions of Carrell on a singular complex projective variety admitting the multiplicative group action, one positively and the other negatively. The results are applied to Chow varieties and we obtain Chow groups of 0-cycles and Lawson homology groups of 1-cycles for Chow varieties. A brief survey on the structure of Chow varieties is included for comparison and completeness. Moreover, we give counterexamples to Shafarevich's problem on the rationality of the irreducible components of Chow varieties.

中文翻译：

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奇异变体和周氏变体的乘性群作用

我们回答了一个关于单数复数射影的两个问题，其中一个是肯定的，另一个是否定的。将结果应用于Chow品种，我们获得了Chow品种的0个周期的Chow组和1个周期的Lawson同源性组。为了比较和完整起见，还对Chow品种的结构进行了简要调查。此外，我们还就Shafarevich关于Chow品种不可约成分的合理性问题给出了反例。