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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