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I was looking at the formula to compute the schubert class of a grassmanian in terms of a more elementary schubert cycles via giambelli's formula, and on the other hand Porteous formula tells us how to compute the determinacy locus of a homomorphism between two vector bundles i.e. when does thier rank drop from maximal rank. And the formulas look the same. Can anyone explain it to me as to how are they exactly related since chern classes are understood to be the pullback of schubert cycles.

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William Fulton, Flags, Schubert polynomials, degeneracy loci, and determinantal formulas, Duke Math J. 65 (1992) 381--420

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