Castelnuovo-Mumford regularity and Gorensteinness of fiber cone
A. V. Jayanthan, Ramakrishna Nanduri
TL;DR
This paper investigates the Castelnuovo-Mumford regularity and Gorenstein properties of the fiber cone, providing bounds, conditions, and formulas to understand its algebraic structure.
Contribution
It introduces new bounds for regularity, conditions for equality with Rees algebra, and a formula for the canonical module of the fiber cone.
Findings
Upper bounds for the regularity of the fiber cone
Conditions for the fiber cone to be Gorenstein
A formula for the canonical module of the fiber cone
Abstract
In this article, we study the Castelnuovo-Mumford regularity and Gorenstein properties of the fiber cone. We obtain upper bounds for the Castelnuovo-Mumford regularity of the fiber cone and obtain sufficient conditions for the regularity of the fiber cone to be equal to that of the Rees algebra. We obtain a formula for the canonical module of the fiber cone and use it to study the Gorenstein property of the fiber cone.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras