Notes on C-graded modules over an affine semigroup ring K[C]

Details Notes on C-graded modules over an affine semigroup ring K[C] Notes on C-graded modules over an affine semigroup ring K[C]

2005-06-22

arxiv.org/abs/math/0506457v2

Mathematics

Commutative Algebra

LARGELY revised version. Sections 4, 5 and most of section 3 are new. 23 pages

Scientific paper

Let $C \subset {\bf N}^d$ be an affine semigroup, and $R=K[C]$ its semigroup ring. This paper is a collection of various results on "$C$-graded" $R$-modules, especially, monomial ideals. For example, we show the following: If $R$ is normal and $I$ is a radical monomial ideal (i.e., $R/I$ is a generalization of Stanley-Reisner rings), then the sequentially Cohen-Macaulay property of $R/I$ is a topological property of the "geometric realization" of the cell complex associated with $I$. Moreover, we can give a squarefree modules/constructible sheaves version of this result.

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