On the Hilbert function of the tangent cone of a monomial curve

2015/06/05 by Marco D’Anna, D'Anna, Marco, Michela Di Marca +3
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Graph theory and applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1506.01797

Abstract

In this paper we study the Hilbert function of \gr_\mathfrakm(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 to improve known results about this problem. To this aim we use certain invariants of the semigroup, with particular regard to its \Apery-set.

Related

• On the Apery sets of monomial curves
• Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three
• On semigroup rings with decreasing Hilbert function
• Tangent cones of numerical semigroup rings
• The ring of differential operators on a monomial curve is a Hopf algebroid