## Geometry & Topology

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

Hsin-Hong Lai

#### Abstract

When the normal bundle $NZ∕X$ is convex with a minor assumption, we prove that genus$−0$ 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 $NZ∕X$ is generated by its global sections. These two main theorems do not hold for arbitrary blow-ups, and counterexamples are included.

#### Article information

Source
Geom. Topol., Volume 13, Number 1 (2009), 1-48.

Dates
Revised: 21 July 2008
Accepted: 5 June 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800174

Digital Object Identifier
doi:10.2140/gt.2009.13.1

Mathematical Reviews number (MathSciNet)
MR2469512

Zentralblatt MATH identifier
1159.14030

Keywords
Gromov–Witten invariants blow-ups

#### Citation

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

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