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arXiv · 1710.07237

The structure of the minimal free resolution of semigroup rings obtained by gluing

Philippe Gimenez·Hema Srinivasan
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Abstract

We construct a minimal free resolution of the semigroup ring k[C] in terms of minimal resolutions of k[A] and k[B] when is a numerical semigroup obtained by gluing two numerical semigroups and . Using our explicit construction, we compute the Betti numbers, graded Betti numbers, regularity and Hilbert series of k[C], and prove that the minimal free resolution of k[C] has a differential graded algebra structure provided the resolutions of k[A] and k[B] possess them. We discuss the consequences of our results in small embedding dimensions. Finally, we give an extension of our main result to semigroups in N^n

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Philippe Gimenez, Hema Srinivasan. 2017-10-19. The structure of the minimal free resolution of semigroup rings obtained by gluing. https://arxiv.org/abs/1710.07237

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