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Generic behaviour of asymptotically holomorphic Lefschetz pencils
Amorós Torrent, Jaume; Muñoz, Vicente; Presas, Francisco
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
Symplectic manifolds
symplectic manifold
Lefschetz hyperplane theorem
asymptotically holomorphic
Varietats simplèctiques
Classificació AMS::57 Manifolds and cell complexes {For complex manifolds, see 32Qxx}
Attribution-NonCommercial-NoDerivs 2.5 Spain
World Scientific

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