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Paper IPM / M / 8423  


Abstract:  
In Helm and Miller (2003, Section 8), the authors posed the problem of which
faces of a saturated affine semigroup Q correspond to prime
ideals associated to the local cohomology module
H^{i}_{I}(ω_{R}) where ω_{R} is the canonical module
of the semigroup ring R = k[Q], k a field, and I is a
monomial ideal in R. In this paper we will give a solution in
the case that Q is simplicial. We will also consider a similar
problem for attached primes of the local cohomology module
H^{i}_{m}(M) where M is a squarefree module (in sense of
Definition 2.7) and m is the homogeneous maximal ideal of R. As
a result, we will show that for a squarefree monomial ideal I in
a normal simplicial semigroup ring R and each integer i ≥ 0,
we have Ass H^{i}_{I}(ω_{R}) = Att H^{d−i}_{m}(R/ I)
where d= dim R.
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