The minimal free resolution of fat almost complete intersections in P1XP1. (on Line Dec 2016)

A current research theme is to compare symbolic powers of an ideal I withthe regular powers of I. In this paper, we focus on the case that I = I_X is an idealdefining an almost complete intersection (ACI) set of points X in P1XP1. In particular,we describe a minimal free bigraded resolution of a non arithmetically Cohen-Macaulay(also non homogeneus) set Z of fat points whose support is an ACI generalizing Corollary4.6 given in [5] for homogeneous sets of triple points. We call Z a fat ACI. We also showthat its symbolic and ordinary powers are equal, i.e, I_Z^{(m)}= I_Z^mfor any $m\geq1$.