Abstract
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.
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Martini, G., Taylor, W. 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces. J. High Energ. Phys. 2015, 61 (2015). https://doi.org/10.1007/JHEP06(2015)061
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DOI: https://doi.org/10.1007/JHEP06(2015)061