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Crepant resolutions of Weierstrass threefolds and non-Kodaira fibres

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.

preprint2015arXivOpen access
Andrea Cattaneo
math.AGhep-th
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Andrea Cattaneo

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