Class of rational surfaces in $\mathsf P^4$

Abstract

In this paper, we obtain a complete classification of all rational surfaces embedded in ${\mathsf P}^4$ so that all their exceptional curves are lines. These surfaces are exactely the rational surfaces shown by I.Bauer to project isomorphicaly from ${\mathsf P}^5$ from one of their points, although no a priori reason is known why such a surface should be projectable in this way.