English

Universally defined cycles I

Algebraic Geometry 2024-12-16 v2

Abstract

We introduce and study the notion of universally defined cycles of smooth varieties of dimension dd, 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.

Keywords

Cite

@article{arxiv.2408.06893,
  title  = {Universally defined cycles I},
  author = {Claire Voisin},
  journal= {arXiv preprint arXiv:2408.06893},
  year   = {2024}
}

Comments

Final version, to appear in Indagationes, special volume dedicated to the memory of Jacob Murre

R2 v1 2026-06-28T18:11:45.174Z