Birational cobordism invariance of uniruled symplectic manifolds
By Jianxun Hu, Tian-Jun Li, Y. Ruan. 2006
72 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/87abae68dfb91c886b1d81a8f3a28f1fe17ad4dd
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In Geometry and Topology
- Jonathan Wise
- D. Abramovich
- Dhruv Ranganathan
- Qile Chen
- Steffen Marcus
- David Jensen
- Barbara Fantechi
- Martin Ulirsch
In Mathematical Physics
- Jonathan Wise
- D. Abramovich
- Dhruv Ranganathan
- Qile Chen
- David Jensen
- Steffen Marcus
- Helge Ruddat
- T. Graber
Citations in the corpus
- Birational invariance in logarithmic Gromov–Witten theory (2013, methodology): “e in genus 0 if Zis the transversal intersection of Xwith a smooth subvariety of an ambient homogeneous space. A number of authors, including Maulik-Pandharipande [MP06] and J. Hu, T.J. Li and Y. Ruan[HLR08], considered thebehavior ofinvariants under blowingup using thedegeneration formula. Theorem ”