#### Volume 13, issue 1 (2009)

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

### Hsin-Hong Lai

Geometry & Topology 13 (2009) 1–48
##### Abstract

When the normal bundle ${N}_{Z∕X}$ is convex with a minor assumption, we prove that genus$-0$ GW–invariants of the blow-up ${Bl}_{Z}X$ 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 ${N}_{Z∕X}$ is generated by its global sections. These two main theorems do not hold for arbitrary blow-ups, and counterexamples are included.

##### Keywords
Gromov–Witten invariants, blow-ups
##### Mathematical Subject Classification 2000
Primary: 14N35
Secondary: 53D45, 14E05
##### Publication
Received: 13 March 2008
Revised: 21 July 2008
Accepted: 5 June 2008
Preview posted: 21 October 2008
Published: 1 January 2009
Proposed: Jim Bryan
Seconded: Ron Stern, Lothar Goettsche
##### Authors
 Hsin-Hong Lai Department of Mathematics Brandeis University 415 South Street MS 050 Waltham, MA 02454