Bounding invariants of fat points using a coding theory construction (Q1946168)

Let \(Z\subset{\mathbb P}_K^n\) be a fat point scheme, where \(K\) is a field of characteristic zero. Then \(Z\) defines a linear code, whose minimum Hamming distance is denoted by \(d(Z).\) Moreover we call \(t_i,\) \(1\leq i\leq n,\) the minimum shift for the \(i\)-th module in a graded minimal free resolution of \(R/I_Z.\) The authors study the constraints imposed by \(d(Z)\) on some of these \(t_i\)'s. More precisely they investigate the particular case when \(Z\) is homogeneous and its support is a complete intersection. They give an upper bound on \(t_n\) in terms of minimum distance of its support.