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- Title
Koppelman formulas on flag manifolds and harmonic forms.
- Authors
Samuelsson, Håkan; Seppänen, Henrik
- Abstract
We construct Koppelman formulas on manifolds of flags in $${\mathbb{C}^N}$$ for forms with values in any holomorphic line bundle as well as in the tautological vector bundles and their duals. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding $${\bar{\partial}}$$-equation. We also construct reproducing kernels for harmonic ( p, q)-forms in the case of Grassmannians.
- Subjects
INTEGRAL equations; HOLOMORPHIC functions; VECTOR bundles; FLAG manifolds (Mathematics); ALGEBRAIC varieties; MANIFOLDS (Mathematics); LIE groups
- Publication
Mathematische Zeitschrift, 2012, Vol 272, Issue 3/4, p1087
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0976-6