Birational cobordism invariance of uniruled symplectic manifolds

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.

To appear in Invent. Math

References in corpus (1)

• Hamiltonian S^1 manifolds are uniruled

Cited by in corpus (10)

• On Symplectic Sum Formulas in Gromov-Witten Theory
• Rationally connected $3$-folds and symplectic geometry
• Hamiltonian S^1 manifolds are uniruled
• Comparing Absolute and relative Gromov--Witten invariants
• Orbifold Gromov--Witten theory of weighted blowups
• On the symplectic invariance of log Kodaira dimension
• Welschinger invariants of Blow-ups of symplectic 4-manifolds
• Symplectic geometry and rationally connected 4-folds
• Ruan's Conjecture on Singular symplectic flops
• Uniruled symplectic divisors