Separators of points on algebraic surfaces |
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Authors: | Laura Bazzotti |
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Affiliation: | a Dipartimento di Matematica, Universita degli Studi di Genova, Via Dodecaneso 35, 16146-Genoa, Italy b Departament Matematica Aplicada I, Universitat Politecnica de Catalunya, Av. Diagonal 647, 08028-Barcelona, Spain |
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Abstract: | For a finite set of points X⊆Pn and for a given point P∈X, the notion of a separator of P in X (a hypersurface containing all the points in X except P) and of the degree of P in X, (the minimum degree of these separators) has been largely studied. In this paper we extend these notions to a set of points X on a projectively normal surface S⊆Pn, considering as separators arithmetically Cohen-Macaulay curves and generalizing the case S=P2 in a natural way. We denote the minimum degree of such curves as and we study its relation to . We prove that if S is a variety of minimal degree these two terms are explicitly related by a formula, whereas only an inequality holds for other kinds of surfaces. |
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Keywords: | 14M05 14H50 |
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