English

Essential dimension of isogenies

Algebraic Geometry 2025-03-19 v6

Abstract

We give a lower bound for the essential dimension of isogenies of complex abelian varieties. The bound is sharp in many cases. In particular, the multiplication-by-mm map is incompressible for every m2m\geq 2, confirming a conjecture of Brosnan.

Keywords

Cite

@article{arxiv.2402.15362,
  title  = {Essential dimension of isogenies},
  author = {János Kollár and Ziquan Zhuang},
  journal= {arXiv preprint arXiv:2402.15362},
  year   = {2025}
}

Comments

12 pages. Small changes to the text. To appear in PAMQ (special issue in honor of James McKernan's 60th birthday)

R2 v1 2026-06-28T14:58:24.232Z