Jordan groups and elliptic ruled surfaces

TL;DR

This paper extends Jordan's theorem to the automorphism groups of elliptic ruled surfaces, showing they have bounded finite subgroups, thus answering a question posed by Vladimir L. Popov.

Contribution

It establishes an analogue of Jordan's theorem for elliptic ruled surfaces' automorphism groups, a new result in algebraic geometry.

Findings

Automorphism groups of elliptic ruled surfaces satisfy Jordan's property.

Positive answer to Popov's question on finite subgroups.

Boundedness of finite subgroups in this context.

Abstract

We prove that an analogue of Jordan's theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of elliptic ruled surfaces. This gives a positive answer to a question of Vladimir L. Popov.