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

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

2009-04-10

arxiv.org/abs/0904.1683v2

Mathematics

Commutative Algebra

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

Scientific paper

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.

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