On the Singular Chern Classes of Schubert Varieties Via Small Resolution

We compute the Chern-Schwartz-MacPherson (CSM) class of a Schubert variety in a Grassmannian using a small resolution introduced by Zelevinsky. As a consequence, we show how to compute the Chern-Mather class using a small resolution instead of the Nash blowup. We use these formulas for CSM classes to prove new cases of a positivity conjecture of Aluffi and Mihalcea. Specifically, we show that codimension 1 coefficients in the CSM class of a Schubert cell are strictly positive and give a closed formula for them.