Let K be a field and let n_1,...,n_e be a sequence of positive integers with gcd(n_1,...,n_e) =1 and n_1 <... < n_e. Let A be the coordinate ring of the associated algebroid monomial curve in the affine algebroid e–space over K . In this article assuming that some e–1 terms of n_1,...,n_e form an arithmetic sequence, we compute ( under some mild additional assumptions , see theorem (2.7) for more precise assumptions ) , the h–polynomial ( and hence the Hilbert function) of A explicitly in terms of the standard basis of the semigroup generated by n_1,...,n_e. Our special assumptions are satisfied in the case e = 3 ; in particular, for the class of algebroid monomial space curves, we can write down the h–polynomial and hence the Hilbert function explicitly .

On the h–polynomial of certain monomial curves

TAMONE, GRAZIA
2004-01-01

Abstract

Let K be a field and let n_1,...,n_e be a sequence of positive integers with gcd(n_1,...,n_e) =1 and n_1 <... < n_e. Let A be the coordinate ring of the associated algebroid monomial curve in the affine algebroid e–space over K . In this article assuming that some e–1 terms of n_1,...,n_e form an arithmetic sequence, we compute ( under some mild additional assumptions , see theorem (2.7) for more precise assumptions ) , the h–polynomial ( and hence the Hilbert function) of A explicitly in terms of the standard basis of the semigroup generated by n_1,...,n_e. Our special assumptions are satisfied in the case e = 3 ; in particular, for the class of algebroid monomial space curves, we can write down the h–polynomial and hence the Hilbert function explicitly .
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/208863
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