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

Abstract

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.

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

References in corpus (5)

• GUTs and Exceptional Branes in F-theory - I
• GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
• D-branes at Singularities, Compactification, and Hypercharge
• D-branes at Singularities and String Phenomenology
• Finite Heisenberg Groups from Nonabelian Orbifold Quiver Gauge Theories

Cited by in corpus (2)

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