Essential dimension of isogenies

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-$m$ map is incompressible for every $m\ge 2$, confirming a conjecture of Brosnan.

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