Claire Voisin

activity

20232026

collaborators

4 papers

math.AG2026

On the Chow ring of very general abelian varieties and a question of Pirola

Claire Voisin

We prove that for a very general abelian variety of dimension $\geq 4$ , a divisor $D \in CH^{1} (A)$ that satisfies $D^{2} = 0$ in $CH^{2} (A)$ is of torsion. The same result is a…

math.AG2024

Universally defined cycles I

Claire Voisin

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 r…

math.AG2024

On the smoothability problem with rational coefficients

Olivier Benoist, Claire Voisin

We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to th…

math.AG2023

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

János Kollár, Claire Voisin

We prove in this paper the smoothability of cycles modulo rational equivalence in the Whitney range, that is, when the dimension is strictly smaller than the codimension. We introd…