The goal is a theorem which allows computations analogous to the Thom-Porteous formula for a morphism of coherent sheaves, which are not vector bundles, over a scheme X. In particular if is the subset where either E or F is not a vector bundle, then the goal is to find a class supported on the set

S. Diaz has one method for accomplishing this goal: find a blow up such that the double dual of the pullbacks of E and F, namely and are vector bundles over Hence over
there is a morphism of vector bundles For an appropriate choice of k, apply the Thom-Porteous formula to compute the fundamental class of Then is a class supported on in X. To derive a formula from this construction it suffices to express the Chern classes of and in terms of known information about E and F. A formula for these Chern classes is derived for E and F belonging to a certain class of coherent sheaves.

Thom-Porteous formula, coherent sheaves, intersection theory, Chern class.