Separators of fat points in P{double-struck}n

In this paper we extend the definition of a separator of a point P in Pn to a fat point P of multiplicity m. The key idea in our definition is to compare the fat point schemes Z=m1P1+...+miPi+...+ msPs⊆P{double-struck}n and Z′=m1P1+...+(mi-1)Pi+. ..+msPs. We associate to Pi a tuple of positive integers of length ν=degZ-degZ'. We call this tuple the degree of the minimal separators of Pi of multiplicity mi, and we denote it by …