SMOOTH CURVES LINKED TO THICK CURVES

In this paper we construct smooth irreducible space curves C which lin k geometrically by surfaces of minimal degree containing C to curves G amma of generic embedding dimension three. This produces interesting b ehavior with respect to both C and Gamma. The curves Gamma link to smo oth connected curves by surfaces of low degree but cannot link to smoo th connected curves by surfaces of high degree. The curves C give coun terexamples to a conjecture of Martin-Deschamps and Perrin.