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Betti Numbers for Numerical Semigroup Rings

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Multigraded Algebra and Applications (NSA 2016)

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Abstract

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.

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Acknowledgements

We gratefully acknowledge the use of the Singular [20] software and of the numericalsgps package [21] in GAP [72] for the development of this paper. The author was supported by a fellowship at the Research Institute of the University of Bucharest (ICUB).

We thank Ignacio García-Marco for sending corrections to an initial version of this paper, to Francesco Strazzanti for useful pointers to the literature and to an anonymous referee for suggestions that improved the presentation. A great moral debt is owed to Jürgen Herzog since our joint projects served as an introduction to the topic of this survey and also as a motivation to write it.

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  1. ICUB/Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, Bucharest, Romania

    Dumitru I. Stamate

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  1. Faculty of Mathematics and Computer Science, Ovidius University, Constanţa, Romania

    Viviana Ene

  2. Department of Mathematics, Duke University, Durham, North Carolina, USA

    Ezra Miller

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Stamate, D.I. (2018). Betti Numbers for Numerical Semigroup Rings. In: Ene, V., Miller, E. (eds) Multigraded Algebra and Applications. NSA 2016. Springer Proceedings in Mathematics & Statistics, vol 238. Springer, Cham. https://doi.org/10.1007/978-3-319-90493-1_8

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