Abstract
In this paper we study the Hilbert function of \(\mathrm {gr}_{\mathfrak {m}}(R)\), when R is a numerical semigroup ring or, equivalently, the coordinate ring of a monomial curve. In particular, we prove a sufficient condition for a numerical semigroup ring in order get a non-decreasing Hilbert function, without making any assumption on its embedding dimension; moreover, we show how this new condition allows us to improve known results about this problem. To this end we use certain invariants of the semigroup, with particular regard to its Apéry-set.
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Communicated by Fernando Torres.
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D’Anna, M., Di Marca, M. & Micale, V. On the Hilbert function of the tangent cone of a monomial curve. Semigroup Forum 91, 718–730 (2015). https://doi.org/10.1007/s00233-015-9754-9
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DOI: https://doi.org/10.1007/s00233-015-9754-9