Separators of points on algebraic surfaces

Abstract: For a finite set of points and for a given point , the notion of a separator of in (a hypersurface containing all the points in except ) and of the degree of in , (the minimum degree of these separators) has been largely studied. In this paper we extend these notions to a set of points on a projectively normal surface , considering as separators arithmetically Cohen–Macaulay curves and generalizing the case in a natural way. We denote the minimum degree of such curves as and we study its relation to . We prove that if 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. [Copyright &y& Elsevier]