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

Lai, Hsin-Hong¹

¹ Department of Mathematics, Brandeis University, 415 South Street MS 050, Waltham, MA 02454

Geometry & topology, Tome 13 (2009) no. 1, pp. 1-48.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.1

Keywords: Gromov–Witten invariants, blow-ups

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