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

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

2007-10-22

arxiv.org/abs/0710.3968v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

Given a submanifold Z inside X, let Y be the blow-up of X along Z. When the normal bundle of Z in X is convex with a minor assumption, we prove that genus-zero GW-invariants of Y 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 the normal bundle is generated by global sections. These two main theorems do not hold for arbitrary blow-ups, and counter-examples are included.

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