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 $\text{dim}R/P\geqslant
n-\sum\text{deg}f_i.$ In characteristic 0 the question is open.