On the geometry of C3/D27 and del Pezzo surfaces
Abstract
We clarify some aspects of the geometry of a resolution of the orbifold X = C3/D27, 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 D27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.
0