English

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

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