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We show that the suspended pinch point can be seen as an elliptically fiberedvariety with singular fibers of type I$_2$ over codimension-one points of thebase and a torsionless Mordell--Weil group of rank one. In the F-theoryalgorithm, this corresponds to a Lie group $SU(2)\times U(1)$. We also identifythe matter content as given by the direct sum of the adjoint representation(with zero U($1$)-charge) and the fundamental representation with U($1$)-charge$\pm 1$. We then study the geometry of an SU($2$)$\times$U($1$)-model given bya compact elliptically fibered variety with the singularities of a suspendedpinch point. We describe in detail the crepant resolutions and the network offlops of this geometry. We compute topological invariants including the Eulercharacteristic and Hodge numbers. We also study the weak coupling limit of thisgeometry and show that it corresponds to an orientifold theory with anSp($1$)-stack transverse to the orientifold and two brane-image-branes wrappingthe orientifold.

The suspended pinch point and SU($2$)$\times$U($1$) gauge theories