Singularities of Some Projective Rational Surfaces

Abstract

We discuss the singularities of some rational algebraic surfaces in complex projective space. In particular, we give formulas for the degrees of the various types of singular loci, in terms of invariants of the surface. These enumerative results can be used, on the one hand, to show the existence of singularities in the complex case, and, on the other hand, as an “upper bound” for the singularities that can occur on a real rational surface.