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Journal of the London Mathematical Society Advance Access published online on May 29, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp020
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© 2009 London Mathematical Society

A symplectic isotopy of a Dehn twist on CPn x CPn+1

Emiko Dupont

Department of Mathematics
Stony Brook University
Stony Brook, NY 11794
USA

The complex manifold CPn x CPn+1 with symplectic form {sigma}µ = {sigma}CPn + µ{sigma}CPn+1, where {sigma}CPn and {sigma}CPn+1 are normalized Fubini–Study forms, n isin N and µ > 1 a real number, contains a natural Lagrangian sphere Lµ. We prove that the Dehn twist along Lµ is symplectically isotopic to the identity for all µ > 1. This isotopy can be chosen so that it pointwise fixes a complex hypersurface in CPn x CPn+1 and lifts to the blow-up of CPn x CPn+1 along a complex n-dimensional submanifold.

2000 Mathematics Subject Classification 53D99, 57R17, 14M25, 57R52.

The author was supported by the Danish Research Agency.

Received April 22, 2008; revised February 10, 2009;
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