Some almost homogeneous group actions on smooth complete rational surfaces (Q1263635)

Let B be a Borel subgroup of SL(2,k) and let X be a complete smooth rational surface over an algebraically closed field of characteristic zero. The author classifies all actions of B on X which have an open orbit. She first shows that any such surface with a B action is obtained by blowing up one of the minimal surfaces with a B-action. She then lists all the possible actions on each of the minimal models which have an open orbit. This information is useful for studying SL(2,k)-embeddings. Compact surfaces with open orbits have been classified previously [see, e.g. \textit{J. Potters}, Invent. Math. 8, 244-266 (1969; Zbl 0205.251)]. This paper, however, classifies the actions given the surface and the group.