A Property Of Local Cohomology Modules Of Polynomial Rings

Abstract

Let $R=k[x_1,...,x_n]$ be a polynomial ring over a field $k$ of characteristic $p>0,$ and let $I=(f_1,...,f_s)$ be an ideal of $R.$ We prove that every associated prime $P$ of $H_I^i(R)$ satisfies $\text{dim}R/P⩾n-\sum \text{deg}{f}_i.$ In characteristic 0 the question is open.

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