Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

Journal of Singularities
volume 25 (2022), 456-474

Received: 31 January 2021. Received in revised form: 17 May 2021.

DOI: 10.5427/jsing.2022.25w

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Abstract:

A (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of a generic determinantal variety, and is a fundamental example to study non-isolated 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.

Author(s) information:

Xiping Zhang