On the geometry of C^3/D_27 and del Pezzo surfaces

Details On the geometry of C^3/D_27 and del Pezzo surfaces On the geometry of C^3/D_27 and del Pezzo surfaces

2010-01-17

arxiv.org/abs/1001.2893v2

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged.

Scientific paper

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.

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