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Birational cobordism invariance of uniruled symplectic manifolds

Jianxun Hu·Tian-Jun Li·Yongbin Ruan
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Abstract

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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Jianxun Hu, Tian-Jun Li, Yongbin Ruan. 2006-11-20. Birational cobordism invariance of uniruled symplectic manifolds. https://doi.org/10.1007/s00222-007-0097-3

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