Gin and lex of certain monomial ideals
- Autores: T. Hibi, S. Murai
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 99, Nº 1, 2006, págs. 76-86
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15000
- Enlaces
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Resumen
Let A = K [x1,…,xn] denote the polynomial ring in n variables over a field K of characteristic 0 with each degxi = 1. Given arbitrary integers i and j with 2≤i≤n and 3≤j≤n, we will construct a monomial ideal I ⊂ A such that (i) βk(I) < βk(Gin(I)) for all k < i, (ii) βi(I) = βi(Gin(I)), (iii) βℓ((Gin(I) ) < βℓ((Lex(I)) for all ℓ < j and (iv) βj(Gin(I)) = βj(Lex(I)), where Gin(I) is the generic initial ideal of I with respect to the reverse lexicographic order induced by x1>⋯>xn and where Lex(I) is the lexsegment ideal with the same Hilbert function as I.
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