Frobenius vectors, Hilbert series and gluings

Abdallah Assi; Pedro A. García-Sánchez; Ignacio Ojeda

Frobenius vectors, Hilbert series and gluings

Commutative Algebra 2013-11-11 v1

Authors: Abdallah Assi , Pedro A. García-Sánchez , Ignacio Ojeda

Abstract

Let $S_1$ and $S_2$ be two affine semigroups and let $S$ be the gluing of $S_1$ and $S_2$ . Several invariants of $S$ are then related to those of $S_1$ and $S_2$ ; we review some of the most important properties preserved under gluings. The aim of this paper is to prove that this is the case for the Frobenius vector and the Hilbert series. Applications to complete intersection affine semigroups are also given.

Keywords

affine semigroups gluings Frobenius vector Hilbert series complete intersection semigroup invariants numerical semigroups

Cite

@article{arxiv.1311.1988,
  title  = {Frobenius vectors, Hilbert series and gluings},
  author = {Abdallah Assi and Pedro A. García-Sánchez and Ignacio Ojeda},
  journal= {arXiv preprint arXiv:1311.1988},
  year   = {2013}
}

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10 pages

Frobenius vectors, Hilbert series and gluings

Abstract

Keywords

Cite

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