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This work has two complementary parts, in the first part we compute the localEuler obstruction of generic determinantal varieties and apply this result tocompute the Chern--Schwartz--MacPherson class of such varieties. In the secondpart we compute the Euler characteristic of the stabilization of an essentiallyisolated determinantal singularity (EIDS). The formula is given in terms of thelocal Euler obstruction and Gaffney's $m_{d}$ multiplicity.

The local Euler obstruction and topology of the stabilization of associated determinantal varieties