Restrictions on symplectic fibrations

Details Restrictions on symplectic fibrations Restrictions on symplectic fibrations

2002-03-22

arxiv.org/abs/math/0203232v1

Mathematics

Symplectic Geometry

An appendix written jointly with Kaoru Ono

Scientific paper

Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e. over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove that, under certain assumptions, a Hamiltonian fibration c-splits, i.e. the spectral sequence associated to the fibration collapses at E_2. Moreover, we obtain a new estimate of the rank of flux groups. In the appendix, we provide examples of nonzero Gromov-Witten invariants for blow-ups. As an application, we prove that any Hamiltonian fibration with fibre being projective space CP^5 blown-up along 4-dimensional symplectic submanifold c-splits.

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