Koppelman formulas on Grassmannians
Elin G\"otmark, H{\aa}kan Samuelsson, Henrik Sepp\"anen
TL;DR
This paper develops Koppelman formulas on Grassmannians for various bundles, leading to new vanishing theorems and connections with Bergman kernels, advancing complex geometry and representation theory.
Contribution
It introduces explicit Koppelman formulas on Grassmannians for multiple bundles, enabling new vanishing theorems and linking to Bergman kernels.
Findings
Derived vanishing theorems of Bott-Borel-Weil type
Connected Koppelman formulas to Bergman kernels
Extended formulas to tautological and dual bundles
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 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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Taxonomy
TopicsAdvanced Differential Geometry Research · Mathematics and Applications · Geometric Analysis and Curvature Flows