ON THE CURVES OF CONTACT ON SURFACES IN A PROJECTIVE-SPACE .3.

Suppose a smooth curve C is a set-theoretic complete intersection of t wo surfaces F and G with the multiplicity of F along C less than or eq ual to the multiplicity of G along C, One obtains a relation between t he degrees of C, F and G, the genus of C, and the multiplicity of F al ong C in case F has only ordinary singularities. One obtains (in the c haracteristic zero case) that a nonsingular rational curve of degree 4 in P-3 is not set-theoretically an intersection of 2 surfaces, provid ed one of them has at most ordinary singularities. The same result hol ds for a general nonsingular rational curve of degree greater than or equal to 5.