Castelnuovo-Mumford Regularity of the Fiber Cone for good filtrations

TL;DR

This paper explores the relationships between various algebraic invariants such as Castelnuovo-Mumford regularity, Rees algebra, and fiber cone in the context of good filtrations, revealing deep connections in algebraic geometry.

Contribution

It establishes new relationships between invariants like regularity, reduction number, and local cohomology for good filtrations, extending understanding of their interplay.

Findings

Connected the regularity of fiber cone with Rees algebra and associated graded ring.

Derived bounds and equalities relating regularity and reduction number.

Provided insights into the vanishing of local cohomology for good filtrations.

Abstract

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