Resumen de Gin and lex of certain monomial ideals

T. Hibi, S. Murai

• 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.