JP Journal of Algebra, Number Theory and Applications
Volume 38, Issue 4, Pages 415 - 430
(August 2016) http://dx.doi.org/10.17654/NT038040415 |
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SOME RESULTS ON CASTELNUOVO-MUMFORD REGULARITY OF THE FIBER CONE
P. H. Lima and V. H. Jorge Pérez
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Abstract: In this paper, we show, for the case of good filtration of ideals, that the relation between the invariants characterizing the homogeneous vanishing of the local cohomology of the Rees algebra and the associated graded ring behaves similarly to the case of adic-filtration. Moreover, we obtain, in certain cases, inequalities (possibly the equality) between the Castelnuovo-Mumford regularity of the fiber cone and the regularity of the associated graded ring as is a good filtration. For instance, if is the analytic spread of and then we show
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Keywords and phrases: Castelnuovo-Mumford regularity, fiber cone, associated graded ring, Rees algebra, good filtration, reduction number. |
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