Minimal free resolutions and asymptotic behavior of multigraded regularity

Details Minimal free resolutions and asymptotic behavior of multigraded regularity Minimal free resolutions and asymptotic behavior of multigraded regularity

2006-06-13

arxiv.org/abs/math/0606312v2

Mathematics

Commutative Algebra

Final version to appear in J. Algebra; 18 pages

Scientific paper

Let S be a standard N^k-graded polynomial ring over a field. Let I be a multigraded homogeneous ideal in S and let M be a finitely generated Z^k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I^nM is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

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