English

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

Commutative Algebra 2016-06-22 v2 Combinatorics

Abstract

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.

Keywords

Cite

@article{arxiv.0904.1683,
  title  = {Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals},
  author = {Victor Reiner and Dumitru I. Stamate},
  journal= {arXiv preprint arXiv:0904.1683},
  year   = {2016}
}

Comments

31 pages, 1 figure. Minor changes from previous version. To appear in Advances in Mathematics