# Almost homogeneous varieties of Albanese codimension one

Research paper by Bruno Laurent

Indexed on: 20 Mar '20Published on: 19 Mar '20Published in: arXiv - Mathematics - Algebraic Geometry

#### Abstract

We classify almost homogeneous normal varieties of Albanese codimension $1$, defined over an arbitrary field. We prove that such a variety has a unique normal equivariant completion. Over a perfect field, the group scheme of automorphisms of this completion is smooth, except in one case in characteristic $2$, and we determine its (reduced) neutral component.