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Aug 27, 2016 at 16:11 vote accept xin fu
Aug 26, 2016 at 21:10 comment added Will Sawin @xinfu A trivial elliptic fibration does not have monodromy. But an isotrivial fibration does. However, the mondromy must be contained in the automorphism group of the curve. This explains the restrictions I wrote down on the fiber type.
Aug 26, 2016 at 15:20 comment added xin fu It seems that isotrivial elliptic fibration doesn't have monodramy. But according to Kodaira, the type of singular fiber is determined by the monodramy.
Aug 26, 2016 at 14:50 history answered Will Sawin CC BY-SA 3.0