The Gaussian Map for Rational Ruled Surfaces

Jeanne Duflot, Rick Miranda
1992 Transactions of the American Mathematical Society  
In this paper the Gaussian map <P: A2 H°{C, K) -* H°{C, 3K) of a smooth curve C lying on a minimal rational ruled surface is computed. It is shown that the corank of O is determined for almost all such curves by the rational surface in which it lies. Hence, except for some special cases, a curve cannot lie on two nonisomorphic minimal rational ruled surfaces.
doi:10.2307/2154174 fatcat:pek5nuogcveingifra2hwhxlc4