  We investigate the classical moduli space of D-branes on a nonabelian
Calabi-Yau threefold singularity and find that it admits topology-changing
transitions. We construct a general formalism of worldvolume field theories in
the language of quivers and give a procedure for computing the enlarged Kahler
cone of the moduli space. The topology changing transitions achieved by varying
the Fayet-Iliopoulos parameters correspond to changes of linearization of a
geometric invariant theory quotient and can be studied by methods of algebraic
geometry. Quite surprisingly, the structure of the enlarged Kahler cone can be
computed by toric methods. By using this approach, we give a detailed
discussion of two low-rank examples.
