Universally defined cycles I

2024/08/13 by Claire Voisin, Voisin, Claire
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2408.06893

openalex publication_date 2024/08/13 · openalex created_date 2024/12/21 · openalex updated_date 2026/07/28

Abstract

We introduce and study the notion of universally defined cycles of smooth varieties of dimension d, and prove that they are given by polynomials in the Chern classes. A similar result is proved for universally defined cycles on products of smooth varieties. We also state a conjectural explicit form for universally defined cycles on powers of smooth varieties, and provide some steps towards establishing it.

Related

• Flat pushforwards of Chern classes and the smoothability of cycles below the middle dimension
• Overconvergent Chern Classes and Higher Cycle Classes
• Cycles and Commutative Algebra
• Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map
• Non-divisible cycles on products of very general Abelian varieties