No codimension-one multiple fibers exist in Lagrangian fibrations over projective space; in Calabi-Yau fibrations on simply-connected K-trivial varieties, the only possible exception is one multiplicity-2 fiber over the projective line.
Multiple fibres on surfaces: geometry, hyperbolic and arithmetic aspects.Manuscr
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Obstructions for codimension one multiple fibers of Lagrangian and Calabi--Yau fibrations
No codimension-one multiple fibers exist in Lagrangian fibrations over projective space; in Calabi-Yau fibrations on simply-connected K-trivial varieties, the only possible exception is one multiplicity-2 fiber over the projective line.