Bott-Chern Forms and Arithmetic Intersections

Abstract

Let \E : 0 --> S --> E --> Q --> 0 be a short exact sequence of hermitian vector bundles with metrics on S and Q induced from that on E. We compute the Bott-Chern form of \E corresponding to any characteristic class, assuming E is projectively flat. The result is used to obtain a new presentation of the Arakelov Chow ring of the arithmetic grassmannian.

22 pages, LaTex, fonts corrected, to appear in L'Enseignement Mathematique

References in corpus (1)

• Arithmetic Intersection Theory on Flag Varieties

Cited by in corpus (4)

• Schubert polynomials and Arakelov theory of symplectic flag varieties
• Complex Chern--Simons bundles in the relative setting
• Algebras of curvature forms on homogeneous manifolds
• Schubert polynomials and Arakelov theory of orthogonal flag varieties