In this article, we consider the problem of lifting the GW theory of a symplectic divisor to that of the ambient manifold in the context of symplectic birational geometry. In particular, we generalize Maulik–Pandharipande’s relative/absolute correspondence to relative-divisor/absolute correspondence. Then, we use it to lift a minimal uniruled invariant of a divisor to that of the ambient manifold.
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Acknowledgements The authors would like to thank Dusa McDuff and Aleksey Zinger for their interest in this paper and for their numerous suggestions which corrected a number of mistakes and greatly improved the presentation. We are also grateful to Davesh Maulik for useful discussions. Both authors are supported by NSF.
© 2013, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.
- Birational symplectic geometry
- Gromov–Witten invariants
- Symplectic divisor
- Uniruled invariant