Flat pushforwards of Chern classes and the smoothability of cycles below the middle dimension

• 成果类型: Article
• 署名作者: Kollar, Janos; Voisin, Claire
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.200.2.7
• 发表日期: 2024
• 页码: 771-797
• 关键词: algebraic cycles; torsion index; subvarieties; RESOLUTION

摘要

We prove in this paper the smoothability of cycles modulo rational equivalence below the middle dimension, that is, when the dimension is strictly smaller than the co dimension. We introduce and study the class of cycles obtained as flat pushforwards of Chern classes (or equivalently, flat pushforwards of products of divisors) and prove that they are smooth- able below the middle dimension. Our main result is that all cycles (of any dimension) on a smooth projective variety are flat pushforwards of Chern classes. In the case of abelian varieties, one can even restrict to smooth pushforwards of Chern classes.