Generic behavior of asymptotically holomorphic Lefschetz pencils.



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Amorós, Jaume and Muñoz, Vicente and Presas, Francisco (2004) Generic behavior of asymptotically holomorphic Lefschetz pencils. The Journal of Symplectic Geometry, 2 (3). pp. 377-392. ISSN 1527-5256

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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.

Item Type:Article
Uncontrolled Keywords:Symplectic; Lefschetz pencil; Asymptotically holomorphic
Subjects:Sciences > Mathematics > Geometry
ID Code:21175
Deposited On:30 Apr 2013 17:15
Last Modified:12 Dec 2018 15:13

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