Publication: Generic behavior of asymptotically holomorphic Lefschetz pencils.
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Publication Date
2004
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International Press
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Abstract
We prove that the vanishing spheres of the Lefschetz pen-
cils constructed by Donaldson on symplectic manifolds of any
dimension are conjugated under the action of the symplec-
tomorphism 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 triv-ial vanishing spheres in these pencils. To develop the proof,we discuss some basic topological properties of the space of asymptotically holomorphic transverse sections.
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