Chern class formulas for $G_2$ Schubert loci
Abstract
We define degeneracy loci for vector bundles with structure group , and give formulas for their cohomology (or Chow) classes in terms of the Chern classes of the bundles involved. When the base is a point, such formulas are part of the theory for rational homogeneous spaces developed by Bernstein-Gelfand-Gelfand and Demazure. This has been extended to the setting of general algebraic geometry by Giambelli-Thom-Porteous, Kempf-Laksov, and Fulton in classical types; the present work carries out the analogous program in type . We include explicit descriptions of the flag variety and its Schubert varieties, and several computations, including one that answers a question of W. Graham. In appendices, we collect some facts from representation theory and compute the Chow rings of quadric bundles, clarifying a previous computation of Edidin and Graham.
Keywords
Cite
@article{arxiv.0712.2641,
title = {Chern class formulas for $G_2$ Schubert loci},
author = {Dave Anderson},
journal= {arXiv preprint arXiv:0712.2641},
year = {2011}
}
Comments
35 pages, part of the author's Ph. D. thesis; v2 includes streamlined exposition and modified conventions, and excludes tables of formulas; v3 includes minor expositional changes and a table of G_2 Schubert polynomials based on the polynomials of Billey and Haiman. To appear in Trans. Amer. Math. Soc