Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
THE CANONICAL PENCILS ON HORIKAWA SURFACES DENIS AUROUX
 

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 4-manifolds, or as symplectic
4-manifolds, 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

  

Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collections: Mathematics