# Separators of arithmetically Cohen-Macaulay fat points ${\bf P}^1\times {\bf P}^1$ Academic Article

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### abstract

• Let Z be a set of fat points in P^1 x P^1 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.

• June 2012