Koppelman formulas on Grassmannians

Details Koppelman formulas on Grassmannians Koppelman formulas on Grassmannians

2007-09-11

arxiv.org/abs/0709.1559v2

Mathematics

Complex Variables

sections 5.3 and 6.2 are new

Scientific paper

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 a consequence we obtain some vanishing theorems of the Bott-Borel-Weil
type. We also relate the projection part of our formulas to the Bergman kernels
associated to the line bundles.

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