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In this paper we extend the definition of a separator of a point P in P n to a fat point P of multiplicity m. The key idea in our definition is to compare the fat point schemes + msPs. We associate to P i a tuple of positive integers of length ν = deg Z − deg Z ′. We call this tuple the degree of the minimal separators of P i of multiplicity m i , and we(More)
We initiate the study of extended bicolorings of Steiner triple systems (STS) which start with a k-bicoloring of an STS(v) and end up with a k-bicoloring of an STS(2v + 1) obtained by a doubling construction , using only the original colors used in coloring the subsystem STS(v). By producing many such extended bicolorings, we obtain several infinite classes(More)
If X is a finite set of points in a multiprojective space P n 1 × · · · × P nr with r ≥ 2, then X may or may not be arithmetically Cohen-Macaulay (ACM). For sets of points in P 1 × P 1 there are several classifications of the ACM sets of points. In this paper we investigate the natural generalizations of these classifications to an arbitrary multiprojective(More)
In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a sepa-rator to shifts in the(More)
Let Z be a set of fat points in a multiprojective space P n1 × · · · × P nr. We introduce definitions for the separator of a fat point and the degree of a fat point in this context, and we study some of their properties. Our definition has been picked so that when we specialize to the cases: (a) Z is a reduced set of points in P n , (b) Z is a set of fat(More)
Let Z be a finite set of double points in P 1 × P 1 and suppose further that X, the support of Z, is arithmetically Cohen-Macaulay (ACM). We present an algorithm, which depends only upon a combinatorial description of X, for the bigraded Betti numbers of I Z , the defining ideal of Z. We then relate the total Betti numbers of I Z to the shifts in the graded(More)