Abstract
This survey presents recent results on minimal free resolutions of numerical semigroup rings. We focus on two classes of numerical semigroups where the resolution is explicitly given: Gorenstein semigroups of embedding dimension 4 that are not a complete intersection and semigroups generated by a sequence of integers in arithmetic progression. Finally, we describe how the resolution is constructed when the semigroup is obtained by gluing of two numerical semigroups of smaller embedding dimension. Along the paper, we provide several non-trivial examples to illustrate our results.
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Acknowledgements
The first author was partially supported by Ministerio de Ciencia e Innovación (Spain) MTM2016-78881-P and Consejería de Educación de la Junta de Castilla y León VA128G18.
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Gimenez, P., Srinivasan, H. (2020). Syzygies of Numerical Semigroup Rings, a Survey Through Examples. In: Barucci, V., Chapman, S., D'Anna, M., Fröberg, R. (eds) Numerical Semigroups . Springer INdAM Series, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-030-40822-0_8
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