Intersection of ACM-curves in IP3

摘要

In this note we address the problem of determining the maximum number of points of intersection of two arithmetically Cohen-Macaulay curves in IP3. We give a sharp upper bound for the maximum number of points of intersection of two irreducible arithmetically Cohen-Macaulay curves C, and C,_r in P3 defined by the maximal minors of a / x (t + 1), resp. (t - r) x (t - r + 1), matrix with linear entries, provided C,-r has no linear series of degree d < (r~5+1) and dimension n > t - r.