Singular Chern Classes of Schubert Varieties via Small Resolution
Algebraic Geometry
2010-03-15 v3 Representation Theory
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.
Keywords
Cite
@article{arxiv.0804.0202,
title = {Singular Chern Classes of Schubert Varieties via Small Resolution},
author = {Benjamin F. Jones},
journal= {arXiv preprint arXiv:0804.0202},
year = {2010}
}
Comments
Addressed referee's comments, Section 6.2 contains new material; 35 pages, 3 figures, and 2 tables