Birational cobordism invariance of uniruled symplectic manifolds

Details Birational cobordism invariance of uniruled symplectic manifolds Birational cobordism invariance of uniruled symplectic manifolds

2006-11-20

arxiv.org/abs/math/0611592v3

Mathematics

Symplectic Geometry

To appear in Invent. Math

Scientific paper

10.1007/s00222-007-0097-3

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symplectic manifold together with a symplectic submanifold. A direct consequence is that symplectic uniruledness is a symplectic birational invariant. Here we use Guillemin and Sternberg's notion of cobordism as the symplectic analogue of the birational equivalence.

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