Small resolutions of SU (5)-models in F-theory

Mboyo Esole Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43496

Advances in Theoretical and Mathematical Physics, 17, (6), 1195-1253, 2013
We provide an explicit desingularization and study the resulting fiber geometry of elliptically fibered four-folds defined by Weierstrass models admitting a split ilde {A} _4 singularity over a divisor of the discriminant locus. Such varieties are used to geometrically engineer SU (5) grand unified theories in F-theory. The desingularization is given by a small resolution of singularities. The ilde {A} _4 fiber naturally appears after resolving the singularities in codimension-one in the base. The remaining higher codimension singularities are then beautifully described by a four-dimensional affine binomial variety which leads to six different small resolutions of the elliptically fibered four-fold. These six small resolutions define distinct four-folds connected to each other by a network of flop transitions forming a dihedral group. The location of these exotic fibers in the base is mapped to conifold points of the three-folds that defines the type IIB
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  title={Small resolutions of SU (5)-models in F-theory},
  author={Mboyo Esole, and Shing-Tung Yau},
  booktitle={Advances in Theoretical and Mathematical Physics},
Mboyo Esole, and Shing-Tung Yau. Small resolutions of SU (5)-models in F-theory. 2013. Vol. 17. In Advances in Theoretical and Mathematical Physics. pp.1195-1253.
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