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6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces. (English) Zbl 1388.83862
Summary: We carry out a systematic study of a class of 6D F-theory models and associated Calabi-Yau threefolds that are constructed using base surfaces with a generalization of toric structure. In particular, we determine all smooth surfaces with a structure invariant under a single $$C^*$$ action (sometimes called “T-varieties” in the mathematical literature) that can act as bases for an elliptic fibration with section of a Calabi-Yau threefold. We identify 162,404 distinct bases, which include as a subset the previously studied set of strictly toric bases. Calabi-Yau threefolds constructed in this fashion include examples with previously unknown Hodge numbers. There are also bases over which the generic elliptic fibration has a Mordell-Weil group of sections with nonzero rank, corresponding to non-Higgsable $$U(1)$$ factors in the 6D supergravity model; this type of structure does not arise for generic elliptic fibrations in the purely toric context.

##### MSC:
 83E50 Supergravity 81T20 Quantum field theory on curved space or space-time backgrounds
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