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On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves - MaRDI portal

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On the monotonicity of the Hilbert functions for 4-generated pseudo-symmetric monomial curves

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Publication:6508879

arXiv2302.09356MaRDI QIDQ6508879

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Abstract: In this article we solve the conjecture "Hilbert function of the local ring for a 4 generated pseudo-symmetric numerical semigroup langlen1,n2,n3,n4angle is always non-decreasing when n1<n2<n3<n4". We give a complete characterization to the standard bases when the tangent cone is not Cohen-Macaulay by showing that the number of elements in the standard basis depends on some parameters sj 's we define. Since the tangent cone is not Cohen-Macaulay, non-decreasingness of the Hilbert fuction was not guaranteed, we proved the non-decreasingness from our explicit Hilbert Function computation.





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