We show that the Chern-Schwartz-MacPherson class of a Schubert cell in a Grassmannian is represented by a reduced and irreducible subvariety in each degree. This gives an affirmative answer to a positivity conjecture of Aluffi and Mihalcea.
@article{arxiv.1302.5852,
title = {Positivity of Chern classes of Schubert cells and varieties},
author = {June Huh},
journal= {arXiv preprint arXiv:1302.5852},
year = {2014}
}