On algebra generated by Chern-Bott forms on SL_n/B

1997/08/20 by B. Shapiro, Boris Shapiro, Shapiro, B. +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9708017

AMSTeX, 7 pages, no pictures

arxiv created 1997/08/20 · openalex publication_date 1997/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short note we give an explicit presentation of the algebra A_n generated by the curvature 2-forms of the standard Hermitiam line bundles over SL_n/B as the quotient of the polynomial ring. The difference between A_n and H^*(SL_n/B) reflects the fact that SL_n/B is not a symmetric space. Possible applications of A_n lie in the field of arithmetic intersection theory on flag varieties.

Related

• Bott-Chern Forms and Arithmetic Intersections
• Arithmetic Intersection Theory on Flag Varieties
• Algebras of curvature forms on homogeneous manifolds
• Higher Bott Chern forms and Beilinson's regulator
• An integration formula of Chern forms on quasi-projective varieties