Supporting degrees of multi-graded local cohomolgoy modules

Details Supporting degrees of multi-graded local cohomolgoy modules Supporting degrees of multi-graded local cohomolgoy modules

2008-10-24

arxiv.org/abs/0810.4487v1

Mathematics

Commutative Algebra

This is to appear in the Journal of Algebra

Scientific paper

For a finitely generated graded module $M$ over a positively-graded commutative Noetherian ring $R$, the second author established in 1999 some restrictions, which can be formulated in terms of the Castelnuovo regularity of $M$ or the so-called $a^*$-invariant of $M$, on the supporting degrees of a graded-indecomposable graded-injective direct summand, with associated prime ideal containing the irrelevant ideal of $R$, of any term in the minimal graded-injective resolution of $M$. Earlier, in 1995, T. Marley had established connections between finitely graded local cohomology modules of $M$ and local behaviour of $M$ across $\Proj(R)$. The purpose of this paper is to present some multi-graded analogues of the above-mentioned work.

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