Separators of Arithmetically Cohen-Macaulay fat points in P¹ x P¹

Original · EN

Let Z be a set of fat points in P¹ x P¹ that is also arithmetically Cohen-Macaulay (ACM). We describe how to compute the degree of a separator of a fat point of multiplicity m for each point in the support of Z using only a numerical description of Z. Our formula extends the case of reduced points which was previously known.