CHARACTERISTIC CLASSES OF HOMOGENEOUS ESSENTIAL ISOLATED DETERMINANTAL VARIETIES

. A (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of a generic determinantal variety, and is a fundamental example to study nonisolated singularities. In this paper we study the characteristic classes on these varieties. We give explicit formulas for their Chern-Schwartz-MacPherson classes and Chern-Mather classes via standard Schubert calculus. As corollaries we obtain formulas for their (generic) sectional Euler characteristics, characteristic cycles, and polar classes.