Abstract
Given a finite set of points Γ in Pk−1 not all contained in a hyperplane, the “fitting problem” asks what is the maximum number hyp(Γ) of
these points that can fit in some hyperplane and what is (are) the equation(s)
of such hyperplane(s)? If Γ has the property that any k − 1 of its points
span a hyperplane, then hyp(Γ) = nil(I) + k − 2, where nil(I) is the index of
nilpotency of an ideal constructed from the homogeneous coordinates of the
points of Γ. Note that in P2 any two points span a line, and we find that the
maximum number of collinear points of any given set of points Γ ⊂ P2 equals
the index of nilpotency of the corresponding ideal, plus one.