Intersection of ACM-curves in ℙ3

Abstract

Abstract In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen–Macaulay curves in ℙ3. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen–Macaulay curves Ct and Ct–r   in ℙ3 defined by the maximal minors of a t  × (t + 1), resp. (t – r ) × (t – r + 1), matrix with linear entries, provided Ct–r   has no linear series of degree and dimension n ≥ t – r.