  A geometric realization of a birational map $\psi$ among two complex
projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action
inducing $\psi$ as the natural birational map among two extremal geometric
quotients. In this paper we study geometric realizations of some classic
birational maps --inversion maps, special Cremona transformations, special
birational transformations of type $(2,1)$--, by considering
$\mathbb{C}^*$-actions on certain rational homogeneous spaces and their
subvarieties.
