A formula for the Chern classes of symplectic blow-ups

Details A formula for the Chern classes of symplectic blow-ups A formula for the Chern classes of symplectic blow-ups

2006-01-23

arxiv.org/abs/math/0601547v1

J. London Math. Soc. (2) 76 (2007), 313-330

Mathematics

Symplectic Geometry

19 pages

Scientific paper

It is shown that the formula for the Chern classes (in the Chow ring) of blow-ups of algebraic varieties, due to Porteous and Lascu-Scott, also holds (in the cohomology ring) for blow-ups of symplectic and complex manifolds. This was used by the second-named author in her solution of the geography problem for 8-dimensional symplectic manifolds. The proof equally applies to real blow-ups of arbitrary manifolds and yields the corresponding blow-up formula for the Stiefel-Whitney classes. In the course of the argument the topological analogue of Grothendieck's `formule clef' in intersection theory is proved.

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