Almost Gorenstein homogeneous rings and their $h$-vectors

Akihiro Higashitani

Almost Gorenstein homogeneous rings and their $h$-vectors

Commutative Algebra 2016-03-10 v2

Authors: Akihiro Higashitani

Abstract

In this paper, for the development of the study of almost Gorenstein graded rings, we discuss some relations between almost Gorensteinness of Cohen--Macaulay homogeneous rings and their $h$ -vectors. Concretely, for a Cohen--Macaulay homogeneous ring $R$ , we give a sufficient condition for $R$ to be almost Gorenstein in terms of the $h$ -vector of $R$ and we also characterize almost Gorenstein homogeneous domains with small socle degrees in terms of the $h$ -vector of $R$ . Moreover, we also provide the examples of almost Gorenstein homogeneous domains arising from lattice polytopes.

Keywords

almost Gorenstein ring homogeneous ring h-vector Cohen-Macaulay socle degree lattice polytope

Cite

@article{arxiv.1507.03307,
  title  = {Almost Gorenstein homogeneous rings and their $h$-vectors},
  author = {Akihiro Higashitani},
  journal= {arXiv preprint arXiv:1507.03307},
  year   = {2016}
}

Comments

14 pages, 1 figure, to appear in J. Alg

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