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On monomial curves obtained by gluing

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Abstract

We study arithmetic properties of tangent cones associated to large families of monomial curves obtained by gluing. In particular, we characterize their Cohen-Macaulay and Gorenstein properties and prove that they have non-decreasing Hilbert functions. The results come from a careful analysis of some special Apéry sets of the numerical semigroups obtained by gluing under a condition that we call specific gluing. As a consequence, we complete and extend the results proved by Arslan et al. (in Proc. Am. Math. Soc. 137:2225–2232, 2009) about nice gluings by using different techniques. Our results also allow to prove that for a given numerical semigroup with a non-decreasing Hilbert function and an integer q>1, all extensions of it by q, except a finite number, have non-decreasing Hibert functions.

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Acknowledgements

This work was initiated during a two months stay in the year 2012 of the first author at the Institute of Mathematics of the University of Barcelona (IMUB), in the frame of its program of visiting researchers. Both authors would like to thank the IMUB for its hospitality and support. Finally, we also would like to thank Tere Cortadellas for a careful reading of this manuscript, and the referee for several good suggestions to improve the clarity of the paper.

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Authors and Affiliations

  1. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran

    Raheleh Jafari

  2. Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Santiago Zarzuela Armengou

Authors
  1. Raheleh Jafari
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  2. Santiago Zarzuela Armengou
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Correspondence to Raheleh Jafari.

Additional information

Communicated by Fernando Torres.

Raheleh Jafari was in part supported by a grant from IPM (No. 900130068).

Santiago Zarzuela Armengou was supported by MTM2010-20279-C02-01.

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Jafari, R., Zarzuela Armengou, S. On monomial curves obtained by gluing. Semigroup Forum 88, 397–416 (2014). https://doi.org/10.1007/s00233-013-9536-1

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