Crepant resolutions of Weierstrass threefolds and non-Kodaira fibres

Abstract

In this paper we want to study the non-Kodaira fibres in a smooth equidimensional elliptic threefold. If the morphism to the Weierstrass model of the fibration is crepant, then we can locate the non-Kodaira fibres and give a description of their structure. In particular, they lie over the singular points of the (reduced) discriminant of the fibration and are contraction of a Kodaira fibre, whose type can be predicted using Tate's algorithm.

19 pages, 5 figures

References in corpus (2)

• Small resolutions of SU(5)-models in F-theory
• A new CY elliptic fibration and tadpole cancellation

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