Volume 13, issue 1 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 NZX 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 NZX 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