On Quadrisecant Lines of Threefolds in P

The classical theorem of general projection for surfaces says that a general projection in P of a smooth complex projective surface S of P is a surface F with ordinary singularities i.e. its singular locus is either empty or is a curve γ such that (i) γ is either non singular or has at most a finite number of ordinary triple points; (ii) every smooth point of γ is either a nodal point or a pinch-point of F ; (iii) the general point of γ is a nodal point for F ; (iv) every triple point of γ is an ordinary triple point of F . (see [6], [11]) Moreover γ is empty if and only if S is already contained in a P.