Piecewise lexsegment ideals
Journal Article
·
· Sbornik. Mathematics
- M.V. Lomonosov Moscow State University, Moscow (Russian Federation)
The problem of describing the Hilbert functions of homogeneous ideals of a commutative polynomial ring containing a fixed monomial ideal I is considered. For this purpose the notion of a piecewise lexsegment ideal is introduced generalizing the notion of a lexsegment ideal. It is proved that if I is a piecewise lexsegment ideal, then it is possible to describe the Hilbert functions of homogeneous ideals containing I in a way similar to that suggested by Macaulay for the situation I=0. Moreover, a generalization of extremal properties of lexsegment ideals is obtained (the inequality for the Betti numbers, behaviour under factorization by homogeneous generic forms)
- OSTI ID:
- 21208367
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 11 Vol. 194; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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