Notes on Hilbert-Kunz Multiplicity of Rees Algebras

Abstract

In this paper, we estimate the Hilbert-Kunz multiplicity of the (extended) Rees algebras in terms of some invariants of the base ring. Also, we give an explicit formula for the Hilbert-Kunz multiplicities of Rees algebras over Veronese subrings.

Key Words:

• Hilbert-Kunz multiplicity
• Rees algebra

1991 Mathematics Subject Classification:

• Primary 13H15
• Secondary 13A30
• 13H35

Acknowledgment

The authors are grateful to Professor Kei-ichi Watanabe for giving them valuable informations. The authors would also like to appreciate the referee's reading this manuscript patiently.