ag.algebraic geometry - Can projective hypersurfaces contain linear spaces? How big?

I am in this, rather friendly, situation:

I have a complex projective space $mathbb{P}^n$, and there i have a (possibly non-smooth) hypersurface $S$ defined by one irreducible polynomial $P$ of degree $d$.

What i want is to get information about the existence or not of linear subvarieties of $S$, and their maximal dimension $m$.
I seem to remember the existence of some ways to get bounds on $m$, given $n$ and $d$, but i don't remember anymore and i don't know where to look..