A new approach to the Hilbert function of a 0-dimensional projective scheme

[摘要] To any 0-dimensional, reduced, degree s, projective scheme X we associate a set S-X of sequences of s natural numbers; these sequences turn out to be a suitable permutations of a nondecreasing sequence (d(1), . . . , d(s)), which is in 1-1 correspondence with the first difference Gamma (X) of the Hilbert function of X. The structure of S-X allows us to read geometric properties of X. In its turn, the set S-Gamma of all sequences allowed for at least one scheme X with Gamma (X) = Gamma can be partitioned into equivalence classes, giving information on all the schemes X with Gamma (X) = Gamma. We start to afford the problem of producing all the sequences equivalent to a given one. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-12-24