Event calendar file
School of Mathematics Colloquium
On the Intersection of Annihilator of the Valabrega-Valla Module
by Prof. Tony Joseph Puthenpurakal (I.I.T., Mumbai)
Thursday, March 31, 2011
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-69 )
at Colaba Campus ( AG-69 )
| Description |
Let $(A, \mathfrak{m})$ be a Cohen-Macaulay local ring with an infinite residue field and let $I$ be an $\mathfrak{m}$-primary ideal. If $J=(x_1, \ldots, x_s)$ is a minimal reduction of $I$ then consider the $A$-module
$$\mathcal{V}_I(J) = \bigoplus_{n\geq 1} \frac{I^{n+1} \cap J} {JI^n}.$$
A consequence of a theorem due to Valabrega and Valla is that $\mathcal{V}_I(J) = 0$ if and only if $G_I(A)$ is Cohen-Macaulay. We show that if $G_I(A)$ is not Cohen-Macaulay then
$$\bigcap {\substack {\text{$J$ minimal} \\ \text{reduction of $I$}}} \operatorname{\ann}_A {\mathcal V}_I{J} \qad \text{is} \mathfrak{m} \text{-primary}.$$
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| Organised by | Aravindakshan T |
