Schubert polynomials and Arakelov theory of symplectic flag varieties

2008/08/31 by Harry Tamvakis
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Flag (linear algebra) #Generalized flag variety #Grassmannian #Lie group #Mathematics #Pure mathematics #Schubert calculus #Schubert polynomial #Schubert variety #Symplectic geometry #Variety (cybernetics) #math.AG #math.CO #msc:05E15 #msc:14G40 #msc:14M15

paper · pdf · doi:10.1112/jlms/jdq015

published as J. London Math. Society 82 (2010), 89-109 · 22 pages; final version

openalex publication_date 2010/05/31 · arxiv created 2013/09/06 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Let 𝔛 = Sp 2n/B be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials that represent the Schubert classes in the Borel presentation of the cohomology ring of 𝔛. We use these polynomials to describe the arithmetic Schubert calculus on 𝔛. Moreover, we give a method to compute the natural arithmetic Chern numbers on 𝔛, and show that they are all rational numbers.

Citations

• Some Combinatorial Properties of Schubert Polynomials
• Flags, Schubert polynomials, degeneracy loci, and determinantal formulas
• Bott-Chern Forms and Arithmetic Intersections
• Diophantine Approximation on Abelian Varieties
• Arithmetic intersection theory