6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces

Gabriella Martini; Washington Taylor

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arXiv · 1404.6300

6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces

Gabriella Martini·Washington Taylor

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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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Gabriella Martini, Washington Taylor. 2015-04-20. 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces. https://arxiv.org/abs/1404.6300

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