# Almost homogeneous curves over an arbitrary field

## TL;DR

This paper classifies pairs of seminormal curves and algebraic groups acting on them with dense orbits over any field, and explores their equivariant Picard groups, extending to some non-seminormal cases.

## Contribution

It provides a comprehensive classification of homogeneous curves over arbitrary fields and analyzes their equivariant Picard groups, including partial results for non-seminormal curves.

## Key findings

- Classification of pairs (C,G) with dense G-orbits on seminormal curves over any field
- Determination of the equivariant Picard group for these curves
- Partial classification results for non-seminormal curves

## Abstract

We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We also give a partial classification when $C$ is no longer assumed to be seminormal.