Algebraic subgroups of the group of birational transformations of ruled surfaces

TL;DR

This paper classifies the largest algebraic subgroups within the birational transformation group of ruled surfaces over curves of positive genus.

Contribution

It provides a complete classification of maximal algebraic subgroups of Bir(C×P^1) for curves of positive genus, advancing understanding of birational symmetries.

Findings

Identifies all maximal algebraic subgroups of Bir(C×P^1) for positive genus curves.

Provides a structural classification of these subgroups.

Enhances understanding of birational automorphisms of ruled surfaces.

Abstract

We classify the maximal algebraic subgroups of Bir(CxPP^1), when C is a smooth projective curve of positive genus.