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We construct a general class of Calabi--Yau threefolds from fiber products ofrational elliptic surfaces with section, generalizing a construction of Schoento include all Kodaira fiber types. The resulting threefolds each have twoelliptic fibrations with section over rational elliptic surfaces and blowupsthereof. These elliptic fibrations generally have nonzero Mordell--Weil rank.Each of the elliptic fibrations has a physical interpretation in terms of asix-dimensional F-theory model with one or more non-Higgsable abelian gaugefields. Many of the models in this class have mild singularities that do notadmit a Calabi--Yau resolution; this does not seem to compromise the physicalintegrity of the theory and can be associated in some cases with masslesshypermultiplets localized at the singular loci. In some of these constructions,however, we find examples of abelian gauge fields that cannot be "unHiggsed" toa nonabelian gauge field without producing unphysical singularities that cannotbe resolved. The models studied here can also be used to exhibit T-duality fora class of little string theories.

Non-Higgsable abelian gauge symmetry and F-theory on fiber products of rational elliptic surfaces