Algebras of curvature forms on homogeneous manifolds

Details Algebras of curvature forms on homogeneous manifolds Algebras of curvature forms on homogeneous manifolds

1999-01-19

arxiv.org/abs/math/9901075v1

Mathematics

Algebraic Geometry

8 pages, LATEX, no figures, also available at http://www.matematik.su.se/users/shapiro

Scientific paper

Let C(X) be the algebra generated by the curvature 2-forms of the standard hermitian line bundles over the complex homogeneous manifold X=G/B. We calculate the Hilbert polynomial of C(X) and give its presentation as a quotient of a polynomial ring. In particular, we show the dimension of C(X) is equal to the number of independent subsets of roots in the corresponding root system. As a tool we study a more general algebra associated with a point on a Grassmannian and calculate its Hilbert polynomial as well as its presentation in terms of generators and relations.

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