Singular Chern Classes of Schubert Varieties via Small Resolution

Abstract

We discuss a method for calculating the Chern-Schwartz-MacPherson (CSM) class of a Schubert variety in the Grassmannian using small resolutions introduced by Zelevinsky. As a consequence, we show how to compute the Chern-Mather class and local Euler obstructions using small resolutions instead of the Nash blowup. The algorithm obtained for CSM classes also allows us to prove new cases of a positivity conjecture of Aluffi and Mihalcea.

Addressed referee's comments, Section 6.2 contains new material; 35 pages, 3 figures, and 2 tables

References in corpus (1)

• Modification systems and integration in their Chow groups

Cited by in corpus (2)

• Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells
• From motivic Chern classes of Schubert cells to their Hirzebruch and CSM classes