English

On the smoothability problem with rational coefficients

Algebraic Geometry 2024-10-22 v2

Abstract

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 this problem would be incompatible with the validity of the Hartshorne conjecture on complete intersections in projective space. We also solve unconditionally a symplectic variant of this problem.

Keywords

Cite

@article{arxiv.2405.12620,
  title  = {On the smoothability problem with rational coefficients},
  author = {Olivier Benoist and Claire Voisin},
  journal= {arXiv preprint arXiv:2405.12620},
  year   = {2024}
}

Comments

13 pages, final version

R2 v1 2026-06-28T16:34:02.712Z