Minimal free resolutions and asymptotic behavior of multigraded regularity
Huy Tai Ha, Brent Strunk
Abstract
Let S be a standard Nk-graded polynomial ring over a field. Let I be a multigraded homogeneous ideal in S and let M be a finitely generated Zk-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of InM is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.
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