Castelnuovo–Mumford Regularity and Gorensteinness of 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.

Key Words:

• Associated graded ring
• Canonical module
• Castelnuovo–Mumford regularity
• Fiber cone
• Gorenstein
• Rees algebra

2000 Mathematics Subject Classification:

• 13H10
• 13C15

ACKNOWLEDGMENTS

We would like to sincerely thank the referee for a thorough reading of the manuscript, pointing out some mistakes and suggesting some improvements.

The second author was supported by the Council of Scientific and Industrial Research, India.

Notes

Communicated by I. Swanson.