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On the geometry of C3/∆27 and del Pezzo surfaces

  • Sergio L. Cacciatori
  • Marco Compagnoni
Article

Abstract

We clarify some aspects of the geometry of a resolution of the orbifold \( X = {{{\mathbb{C}^3}} \mathord{\left/{\vphantom {{{\mathbb{C}^3}} {{\Delta_{27}}}}} \right.} {{\Delta_{27}}}} \), 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 ∆27 and the Hessian group and on the study of the behaviour of the Hesse pencil of plane cubic curves under the quotient.

Keywords

Brane Dynamics in Gauge Theories Differential and Algebraic Geometry Intersecting branes models Superstring Vacua 

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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversità degli Studi dell’Insubria22100ComoItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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