Schubert polynomials and Arakelov theory of symplectic flag varieties

Harry Tamvakis

Published 2008-08-09, updated 2013-09-06Version 2

Let X be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which 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.