科研之友
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摘要
Given a finite set of points G in Pk-1 not all contained in a hyperplane, the %26quot;fitting problem%26quot; asks what is the maximum number hyp(Gamma) of these points that can fit in some hyperplane and what is (are) the equation(s) of such hyperplane(s)? If Gamma has the property that any k - 1 of its points span a hyperplane, then hyp(Gamma) = nil(I) + k - 2, where nil(I) is the index of nilpotency of an ideal constructed from the homogeneous coordinates of the points of G. Note that in P-2 any two points span a line, and we find that the maximum number of collinear points of any given set of points Gamma subset of P-2 equals the index of nilpotency of the corresponding ideal, plus one.
- 出版日期2014-2
