In this paper we give a combinatorial characterization of monomial ideals of the polynomial ring in n variables over a field k of characteristic 0, focussing our attention to stable , Borel and lex-segment ideals. We consider the order ideal associated to a monomial ideal consisting of all the terms outside the ideal, which reflects the geometric structure of the reduced union of linear varieties associated to the given monomial ideal, via the well-known lifting-construction due to Hartshorne. To each monomial ideal we associate a numerical character, called E-vector, which gives in a very compact way the `geometric configuration' of the order ideal associated and a canonical system of generators of the given monomial ideal that in the stable case is precisely the minimal system generators.
A characterization of stable and Borel ideals
MARINARI, MARIA GRAZIA;RAMELLA, LUCIANA
2005-01-01
Abstract
In this paper we give a combinatorial characterization of monomial ideals of the polynomial ring in n variables over a field k of characteristic 0, focussing our attention to stable , Borel and lex-segment ideals. We consider the order ideal associated to a monomial ideal consisting of all the terms outside the ideal, which reflects the geometric structure of the reduced union of linear varieties associated to the given monomial ideal, via the well-known lifting-construction due to Hartshorne. To each monomial ideal we associate a numerical character, called E-vector, which gives in a very compact way the `geometric configuration' of the order ideal associated and a canonical system of generators of the given monomial ideal that in the stable case is precisely the minimal system generators.
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