Geometry & Topology

Gromov–Witten invariants of blow-ups along submanifolds with convex normal bundles

Hsin-Hong Lai

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When the normal bundle NZX is convex with a minor assumption, we prove that genus0 GW–invariants of the blow-up BlZX of X along a submanifold Z, with cohomology insertions from X, are identical to GW–invariants of X. Under the same hypothesis, a vanishing theorem is also proved. An example to which these two theorems apply is when NZX is generated by its global sections. These two main theorems do not hold for arbitrary blow-ups, and counterexamples are included.

Article information

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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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

Gromov–Witten invariants blow-ups


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.

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