Subbundles of maximal degree of the normal bundle of algebraic space curves almost complete intersection of special type

Abstract

LetX⊂P 3 be an irreducible smooth curve which is not a complete intersection. The main result of this paper shows that whenX is an a.c.i. of special type, i.e. its homogeneous ideal is generated by three polynomial of the same degreem, and additionallym>2, the subbundles of maximal degree of the normal bundle ofX inP 3 correspond to the singular points of maximal multiplicity of a plane curve which is the image ofX by a map\(X\mathop \to \limits^\varphi P^2 \) (the linear system of the surfaces of minimal degree throughX). In particular this normal bundle is stable. The initial case of this family of curves, i.e. form=3, has been studied by E. Ballico-Ph. Ellia with different methods.