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In this paper we show that there is a close relationship between theinvariants characterizing the homogeneous vanishing of the local cohomology ofthe Rees algebra and the associated graded ring for the good filtrations case.We obtain relationships between the Castelnuovo-Mumford regularity of the fibercone, associated graded ring, Rees algebra and reduction number for the goodfiltrations case.

Castelnuovo-Mumford Regularity of the Fiber Cone for good filtrations