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Koppelman formulas on Grassmannians
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Elin Götmark
Published/Copyright:
January 20, 2010
Abstract
We construct Koppelman formulas on Grassmannians for forms with values in any holomorphic line bundle as well as in the tautological vector bundle and its dual. As an application we obtain new explicit proofs of some vanishing theorems of the Bott-Borel-Weil type by solving the corresponding 
-equation. We also relate the projection part of our formulas to the Bergman kernels associated to the line bundles.
Received: 2008-06-10
Revised: 2008-11-20
Published Online: 2010-01-20
Published in Print: 2010-March
© Walter de Gruyter Berlin · New York 2010
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Articles in the same Issue
- On the torsion of Drinfeld modules of rank two
- Endpoint maximal and smoothing estimates for Schrödinger equations
- Kähler-Ricci flow on stable Fano manifolds
- Area-minimizing vector fields on round 2-spheres
- Koppelman formulas on Grassmannians
- A quotient restriction theorem for actions of real reductive groups
- Graph algebras, Exel-Laca algebras, and ultragraph algebras coincide up to Morita equivalence
- On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
- Über Pro-p-Fundamentalgruppen markierter arithmetischer Kurven
