Geometry & Topology
- Geom. Topol.
- Volume 13, Number 1 (2009), 1-48.
Gromov–Witten invariants of blow-ups along submanifolds with convex normal bundles
When the normal bundle is convex with a minor assumption, we prove that genus GW–invariants of the blow-up of along a submanifold , with cohomology insertions from , are identical to GW–invariants of . Under the same hypothesis, a vanishing theorem is also proved. An example to which these two theorems apply is when is generated by its global sections. These two main theorems do not hold for arbitrary blow-ups, and counterexamples are included.
Geom. Topol., Volume 13, Number 1 (2009), 1-48.
Received: 13 March 2008
Revised: 21 July 2008
Accepted: 5 June 2008
First available in Project Euclid: 20 December 2017
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 14E05: Rational and birational maps
Lai, Hsin-Hong. Gromov–Witten invariants of blow-ups along submanifolds with convex normal bundles. Geom. Topol. 13 (2009), no. 1, 1--48. doi:10.2140/gt.2009.13.1. https://projecteuclid.org/euclid.gt/1513800174