On the Chow Groups of Certain Cubic Fourfolds  

作　　者：Robert LATERVEER 

机构地区：[1]Institut de Recherche Mathématique Avancée,CNRS-Universitd de Strasbourg,7 Rue Rene Descartes,67084 Strasbourg Cedex,France

出　　处：《Acta Mathematica Sinica,English Series》2017年第7期887-898,共12页数学学报（英文版）

摘　　要：This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family. Keywords Algebraic cycles, Chow groups, motives, cubic fourfolds, hyperkiihler varieties, K3 sur- faces, finite-dimensional motiveThis note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family. Keywords Algebraic cycles, Chow groups, motives, cubic fourfolds, hyperkiihler varieties, K3 sur- faces, finite-dimensional motive

关 键 词：Algebraic cycles Chow groups motives cubic fourfolds hyperk?hler varieties K3 surfaces finite-dimensional motive 

分 类 号：O152[理学—数学]