Characteristic Classes of Homogeneous Essential Isolated Determinantal Varieties

TL;DR

This paper derives explicit formulas for characteristic classes of homogeneous essential isolated determinantal varieties, advancing understanding of their singularities and related invariants using Schubert calculus.

Contribution

It provides the first explicit formulas for Chern-Schwartz-MacPherson and Chern-Mather classes of these varieties, connecting singularity theory with Schubert calculus.

Findings

Formulas for Chern-Schwartz-MacPherson classes

Formulas for Chern-Mather classes

Results on sectional Euler characteristics, characteristic cycles, and polar classes

Abstract

The (homogeneous) Essentially Isolated Determinantal Variety is the natural generalization of generic determinantal variety, and is fundamental example to study non-isolated singularities. In this paper we study the characteristic classes on these varieties. We give explicit formulas of 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.