A structure theorem for most unions of complete intersections

Abstract

Using the connections among almost complete intersection schemes, arithmetically Gorenstein schemes and schemes that are a union of complete intersections, we give a structure theorem for the arithmetically Cohen-Macaulay union of two complete intersections of codimension~2, of type $(d_1,e_1)$ and $(d_2,e_2)$ such that $\min \{d_1,e_1\}\ne \min \{d_2,e_2\}$. We apply the results for computing Hilbert functions and graded Betti numbers for such schemes.