  We analyze in detail the case of a marginally stable D-Brane on a collapsed
del Pezzo surface in a Calabi-Yau threefold using the derived category of
quiver representations and the idea of aligned gradings. We show how the
derived category approach to D-branes provides a straight-forward and rigorous
construction of quiver gauge theories associated to such singularities. Our
method shows that a procedure involving exceptional collections used elsewhere
in the literature is only valid if some tachyon-inducing Ext3 groups are zero.
We then analyze in generality a large class of Seiberg dualities which arise
from tilting equivalences. It follows that some (but not all) mutations of
exceptional collections induce Seiberg duality in this context. The same
tilting equivalence can also be used to remove unwanted Ext3 groups and convert
an unphysical quiver into a physical one.
