Abstract
Let π:X→Y be an n-dimensional iterated Kodaira fibration with fiber of genus g and injective monodromy. In [6], it is proved that we can pass to a finite index subgroup of π1(X) to get the base space of an (n+1)-dimensional iterated Kodaira fibration with injective monodromy, and they asked about bounding the index of such a group. We provide a bound on this index.
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