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

✍ Scribed by Giannina Beccari; Carla Massaza

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 172 KB
• Volume: 165
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00019-6

✦ Synopsis

To any 0-dimensional, reduced, degree s, projective scheme X we associate a set SX of sequences of s natural numbers; these sequences turn out to be a suitable permutations of a nondecreasing sequence (d1; : : : ; ds), which is in 1-1 correspondence with the ÿrst di erence 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 of all sequences allowed for at least one scheme X with X = can be partitioned into equivalence classes, giving information on all the schemes X with X = . We start to a ord the problem of producing all the sequences equivalent to a given one.