On the intersection of annihilator of the Valabrega–Valla module

  • Tony J. Puthenpurakal

    Indian Institute of Technology Bombay, Mumbai, India

Abstract

Let be a Cohen–Macaulay local ring with an infinite residue field and let be an -primary ideal. Let be a -superficial sequence \wrt \ . Set

A consequence of a theorem due to Valabrega and Valla is that if and only if the initial forms is a regular sequence. Furthermore this holds if and only if depth . We show that if depth then

Suprisingly we also prove that under the same hypotheses,

Cite this article

Tony J. Puthenpurakal, On the intersection of annihilator of the Valabrega–Valla module. Rend. Sem. Mat. Univ. Padova 135 (2016), pp. 21–37

DOI 10.4171/RSMUP/135-2