On the geometry of C^3/D_27 and del Pezzo surfaces
High Energy Physics - Theory
2016-04-07 v2 Mathematical Physics
Algebraic Geometry
math.MP
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.
Cite
@article{arxiv.1001.2893,
title = {On the geometry of C^3/D_27 and del Pezzo surfaces},
author = {Sergio Luigi Cacciatori and Marco Compagnoni},
journal= {arXiv preprint arXiv:1001.2893},
year = {2016}
}
Comments
23 pages, 5 figures, 2 tables. JHEP style. Added references. Corrected typos. Revised introduction, results unchanged.