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About: Porteous formula     Goto   Sponge   NotDistinct   Permalink

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In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's formula is roughly the special case when the vector bundles are sums of line bundles over projective space. Thom pointed out that the fundamental class must be a polynomial in the Chern classes and found this polynomial in a few special cases, and Porteous found the polynomial in general. proved a more general version, and generalized it further.