Let G a semsisimple connect'ed group over $k$, $B$ a Borel and $P$ a parabolic subgroup of $G$ with Weyl group W_{P}.

For $w\in W_{P}\backslash W/W_{P}$, how can we solve the singularities of $X_{w}=\overline{PwP}/P\subset G/P$?

By solving, the singularities, I want that the the resulting

$\pi:Y\rightarrow X_{w}$

is an isomorphism on $PwP/P$.