Work

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

Year: 2024

Type: article

Abstract: 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 codimension. 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 smoothable 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.

Source: Annals of Mathematics

DOI: 10.4007/annals.2024.200.2.7

Authors: János Kollár, Claire Voisin

Institutions: Princeton University, Centre National de la Recherche Scientifique, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, H2020 European Research Council

Awards: Moduli of Varieties of General Type, Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties