Graded Cohen-Macaulay domains and lattice polytopes with short $h$-vector

Lukas Katthän; Kohji Yanagawa

Graded Cohen-Macaulay domains and lattice polytopes with short $h$-vector

Commutative Algebra 2020-09-02 v3 Combinatorics

Authors: Lukas Katthän , Kohji Yanagawa

Abstract

Let P be a lattice polytope with $h^*$ -vector $(1, h^*_1, h^*_2)$ . In this note we show that if $h_2^* \leq h_1^*$ , then $P$ is IDP. More generally, we show the corresponding statements for semi-standard graded Cohen-Macaulay domains over algebraically closed fields.

Keywords

lattice polytope h*-vector IDP Cohen-Macaulay domain graded ring algebraically closed field

Cite

@article{arxiv.1907.07214,
  title  = {Graded Cohen-Macaulay domains and lattice polytopes with short $h$-vector},
  author = {Lukas Katthän and Kohji Yanagawa},
  journal= {arXiv preprint arXiv:1907.07214},
  year   = {2020}
}

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