 
Summary: THE CANONICAL PENCILS ON HORIKAWA SURFACES
DENIS AUROUX
Abstract. We calculate the monodromies of the canonical Lefschetz
pencils on a pair of homeomorphic Horikawa surfaces. We show in par
ticular that the (pluri)canonical pencils on these surfaces have the same
monodromy groups, and are related by a "partial twisting" operation.
1. Introduction
Horikawa surfaces are minimal complex surfaces of general type which
realize the equality case in Noether's inequality c2
1 2pg  4. While their
classification as complex surfaces has been completed a long time ago [16],
the topology of these surfaces viewed as smooth 4manifolds, or as symplectic
4manifolds, remains mysterious. In this paper we consider two specific
Horikawa surfaces:
Definition 1.1. Denote by X1 a double cover of CP1
×CP1
branched along
a smooth algebraic curve C1 of bidegree (6, 12). Denote by X2 a double cover
of the Hirzebruch surface F6 = P(OP1 OP1 (6)) branched along C2,
where is the exceptional section of F6 ( · = 6), and C2 is
