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Schubert polynomials and Arakelov theory of orthogonal flag varieties

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Abstract

We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of the orthogonal flag variety \({\mathfrak X={\rm SO}_N/B}\). We use these polynomials to describe the arithmetic Schubert calculus on \({\mathfrak X}\). Moreover, we give a method to compute the natural arithmetic Chern numbers on \({\mathfrak X}\), and show that they are all rational numbers.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 1301 Mathematics Building, College Park, MD, 20742, USA

    Harry Tamvakis

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  1. Harry Tamvakis
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Correspondence to Harry Tamvakis.

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The author was supported in part by National Science Foundation Grant DMS-0901341.

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Tamvakis, H. Schubert polynomials and Arakelov theory of orthogonal flag varieties. Math. Z. 268, 355–370 (2011). https://doi.org/10.1007/s00209-010-0676-7

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  • DOI: https://doi.org/10.1007/s00209-010-0676-7

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