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

Lai, Hsin-Hong

doi:10.2140/gt.2009.13.1

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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

DOI: 10.2140/gt.2009.13.1

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

References

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

Volume 13, issue 1 (2009)