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A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled}if there is a nonzero genus zero GW invariant involving a point constraint. Weprove that symplectic uniruledness is invariant under symplectic blow-up andblow-down. This theorem follows from a general Relative/Absolute correspondencefor a symplectic manifold together with a symplectic submanifold. A directconsequence is that symplectic uniruledness is a symplectic birationalinvariant. Here we use Guillemin and Sternberg's notion of cobordism as thesymplectic analogue of the birational equivalence.Comment: To appear in Invent. Mat

Birational cobordism invariance of uniruled symplectic manifolds