Intersection of ACM-curves in P^3

In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen-Macaulay curves in ${\text{PP}}^3$. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen-Macaulay curves $C_t$ and $C_{t-r}$ in ${\text{PP}}^3$ defined by the maximal minors of a $t\times (t+1)$, resp. $(t-r) \times (t-r+1)$,matrixwithlinearentries,provided$C_{t-r}$ has no linear series of degree $d\le \left(\genfrac{}{}{0px}{}{t-r+1}{3}\right)$ and dimension $n\ge t-r$.