Notes on C-graded modules over an affine semigroup ring K[C]
Kohji Yanagawa
Abstract
Let C ⊂ Nd 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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