## Abstract

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 singular cohomology ring) for blow-ups of symplectic and complex manifolds. This was used by the second 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. © 2007 London Mathematical Society.

Original language | English |
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Pages (from-to) | 313-330 |

Journal | Journal of the London Mathematical Society |

Volume | 76 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 |