Intersection of ACM-curves in P^3

Abstract

In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen-Macaulay curves in $\PP^3$. 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 $\PP^3$ defined by the maximal minors of a $t\times (t+1)$, resp. $(t-r)\times (t-r+1)$, matrix with linear entries, provided $C_{t-r}$ has no linear series of degree $d\le \left(\genfrac{}{}{0ex}{}{t-r+1}{3}\right)$ and dimension $n\ge t-r$.

15 pages