The canonical pencils on Horikawa surfaces

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We calculate the monodromies of the canonical Lefschetz pencils on a pair of homeomorphic Horikawa surfaces. We show in particular that the (pluri)canonical pencils on these surfaces have the same monodromy groups, and are related by a "partial twisting" operation.
This is the version published by Geometry & Topology on 29 November 2006

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