Essential dimension of isogenies

2024/02/23 by Kollár, János, Zhuang, Ziquan · 5 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.15362

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≥ 2, confirming a conjecture of Brosnan.

Cited by

• Actions of (ℤ/4)⁴ on rationally connected threefolds
• Essential dimensions of polarized endomorphisms of abelian varieties
• On abelian extensions of finite abelian subgroups of Cremona groups
• Finite abelian groups acting on rationally connected threefolds II: groups of K3 type
• The essential and the Cremona dimensions of a group

Related

• Essential dimension of abelian varieties over number fields
• Derived isogenies between abelian varieties
• Abelian varieties with real multiplication: classification and isogeny classes over finite fields
• Size of isogeny classes of abelian varieties of Lubin-Tate type
• Une minoration du minimum essentiel sur les varietes abeliennes