The multiplicative group action on singular varieties and Chow varieties期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The multiplicative group action on singular varieties and Chow varieties

Authors:	Wenchuan Hu

Affiliation:	1. Laboratoire de Mathématiques Paul Painlevé, Université de Lille, 59655 Villeneuve d''Ascq Cedex, France;2. Department of Mathematics Education, Korea National University of Education, 28173 Cheongju, South Korea;3. Institut für Algebra, Fachrichtung Mathematik, TU Dresden, 01062 Dresden, Germany;4. Department of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel;1. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany;2. Institut Denis Poisson, CNRS, Université de Tours, Université d''Orléans, Parc de Grandmont, 37200 Tours, France;1. School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom;2. Department of Mathematics, University of Manchester, Oxford Road M13 6PL, United Kingdom;1. Department of Mathematics, Pedagogical University of Cracow, Podchora??ych 2, PL-30-084 Cracow, Poland;2. Jagiellonian University, Faculty of Mathematics and Computer Science, ?ojasiewicza 6, PL-30-348 Cracow, Poland

Abstract:	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.

Keywords:	Holomorphic vector field Multiplicative group action Algebraic cycle Chow group Chow variety
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