On the intersection of annihilator of the Valabrega–Valla module
Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 21-37.

Let (A,𝔪) be a Cohen–Macaulay local ring with an infinite residue field and let I be an 𝔪-primary ideal. Let 𝐱=x 1 ,...,x r be a A-superficial sequence \wrt \ I. Set

𝒱 I (𝐱)= n1 I n+1 (𝐱) 𝐱I n .
A consequence of a theorem due to Valabrega and Valla is that 𝒱 I (𝐱)=0 if and only if the initial forms x 1 * ,...,x r * is a G I (A) regular sequence. Furthermore this holds if and only if depth G I (A)r. We show that if depth G I (A)<r then
𝔞 r (I)= 𝐱=x 1 ,...,x r is aA- superficial sequence with respect to I ann A 𝒱 I (𝐱) is 𝔪- primary .
Suprisingly we also prove that under the same hypotheses,
n1 𝔞 r (I n ) is also 𝔪- primary .

DOI : 10.4171/RSMUP/135-2
Classification : 13
Mots clés : Blow-up algebras, multiplicity theory, core
Puthenpurakal, Tony 1

1 Indian Institute of Technology Bombay, MUMBAI, INDIA
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     title = {On the intersection of annihilator of the {Valabrega{\textendash}Valla} module},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {21--37},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {135},
     year = {2016},
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Puthenpurakal, Tony. On the intersection of annihilator of the Valabrega–Valla module. Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 21-37. doi : 10.4171/RSMUP/135-2. http://www.numdam.org/articles/10.4171/RSMUP/135-2/

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