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The canonical pencils on Horikawa surfaces

Denis Auroux
Geometry & Topology 10 (2006) 2173–2217
DOI: 10.2140/gt.2006.10.2173

arXiv: math.GT/0605692
Abstract

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.

Keywords
Horikawa surfaces, Lefschetz pencils, monodromy
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D35, 14D05
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Publication
Received: 28 May 2006
Revised: 25 September 2006
Accepted: 22 October 2006
Published: 29 November 2006
Proposed: Rob Kirby
Seconded: Ronald Fintushel, Ronald Stern
Authors
Denis Auroux
Department of Mathematics
MIT
Cambridge, MA 02139
USA