Open Access
September 2004 Generic behavior of asymptotically holomorphic Lefschetz pencils
Jaume Amor\'os, Vicente Mu\~noz, Francisco Presas
J. Symplectic Geom. 2(3): 377-392 (September 2004).


We prove that the vanishing spheres of the Lefschetz pencils constructed by Donaldson on symplectic manifolds of any dimension are conjugated under the action of the symplectomorphism group of the fiber. More precisely, a number of generalized Dehn twists may be used to conjugate those spheres. This implies the non-existence of homologically trivial vanishing spheres in these pencils. To develop the proof, we discuss some basic topological properties of the space of asymptotically holomorphic transverse sections.


Download Citation

Jaume Amor\'os. Vicente Mu\~noz. Francisco Presas. "Generic behavior of asymptotically holomorphic Lefschetz pencils." J. Symplectic Geom. 2 (3) 377 - 392, September 2004.


Published: September 2004
First available in Project Euclid: 14 June 2005

zbMATH: 1078.53085
MathSciNet: MR2131641

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 3 • September 2004
Back to Top