  We clarify some aspects of the geometry of a resolution of the orbifold X =
C3/D_27, the noncompact complex manifold underlying the brane quiver standard
model recently proposed by Verlinde and Wijnholt. We explicitly realize a map
between X and the total space of the canonical bundle over a degree 1 quasi del
Pezzo surface, thus defining a desingularization of X. Our analysis relys
essentially on the relationship existing between the normalizer group of D_27
and the Hessian group and on the study of the behaviour of the Hesse pencil of
plane cubic curves under the quotient.
