On the Chow group of zero-cycles of a generalized Kummer variety

2015/07/18 by Lin, Hsueh-Yung
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1507.05155

Abstract

For a generalized Kummer variety X of dimension 2n, we will construct for each 0 < i < n some co-isotropic subvarieties in X foliated by i-dimensional constant cycle subvarieties. These subvarieties serve to prove that the rational orbit filtration introduced by Voisin on the Chow group of zero-cycles of a generalized Kummer variety coincides with the induced Beauville decomposition from the Chow ring of abelian varieties. As a consequence, the rational orbit filtration is opposite to the conjectural Bloch-Beilinson filtration for generalized Kummer varieties.

Related

• Remarks and questions on coisotropic subvarieties and 0-cycles of hyper-Kähler varieties
• Algebraic cycles on a generalized Kummer variety
• 0-cycles and sheaves on abelian surfaces
• A Filtration of the Chow Group of Zero-Cycles for a Product of Curves and an Abelian Variety
• A filtration on the higher Chow group of zero cycles on an abelian variety