The multiplicative group action on singular varieties and Chow varieties

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Hu, Wenchuan¹ 

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

关键词: Holomorphic vector field;    Multiplicative group action;    Algebraic cycle;    Chow group;    Chow variety;   

DOI  :  10.1016/j.jpaa.2021.106667

来源: Elsevier

【 摘 要 】

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. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free