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Abstract: In this paper we extend the definition of a separator of a point P in P^n toa fat point P of multiplicity m. The key idea in our definition is to comparethe fat point schemes Z = m 1P 1 +

. + m iP i +

+ m sP s in P^n and Z- =m 1P 1 +

. + m i-1P i +

+ m sP s. We associate to P i a tuple ofpositive integers of length v = deg Z - deg Z-. We call this tuple the degreeof the minimal separators of P i of multiplicity m i, and we denote it bydeg ZP i = d 1,

.,d v. We show that if one knows deg ZP i and theHilbert function of Z, one will also know the Hilbert function of Z-. We alsoshow that the entries of deg ZP i are related to the shifts in the lastsyzygy module of I Z. Both results generalize well known results about reducedsets of points and their separators.

Autor: Elena Guardo, Lucia Marino, Adam Van Tuyl


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