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LOCAL COHOMOLOGY OF MULTI-REES ALGEBRAS, JOINT REDUCTION NUMBERS AND PRODUCT OF COMPLETE IDEALS

Published online by Cambridge University Press:  18 October 2016

PARANGAMA SARKAR
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India email parangama@math.iitb.ac.in
J. K. VERMA
Affiliation:
Department of Mathematics, Indian Institute of Technology Bombay, Mumbai, Maharashtra 400076, India email jkv@math.iitb.ac.in

Abstract

We find conditions on the local cohomology modules of multi-Rees algebras of admissible filtrations which enable us to predict joint reduction numbers. As a consequence, we are able to prove a generalization of a result of Reid, Roberts and Vitulli in the setting of analytically unramified local rings for completeness of power products of complete ideals.

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© 2016 by The Editorial Board of the Nagoya Mathematical Journal  

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LOCAL COHOMOLOGY OF MULTI-REES ALGEBRAS, JOINT REDUCTION NUMBERS AND PRODUCT OF COMPLETE IDEALS
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