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Cohomology of line bundles on horospherical varieties

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A horospherical variety is a normal algebraic variety where a connected reductive algebraic group acts with an open orbit isomorphic to a torus bundle over a flag variety. In this article we study the cohomology of line bundles on complete horospherical varieties. The main tool in this article is the machinery of Grothendieck–Cousin complexes, and we also prove a Künneth-like formula for local cohomology.

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Acknowledgements

We would like to thank Michel Brion for valuable discussions and many critical comments. We also thank the anonymous referee for numerous comments and suggestions. The first author would also like to thank Max Planck Institute for Mathematics (Bonn) for the postdoctoral fellowship, and for providing very pleasant hospitality.

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  1. Narasimha Chary Bonala

    Present address: Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany

Authors and Affiliations

  1. Max Planck Institute for Mathematics, Vivatsgasse 7, Bonn, Germany

    Narasimha Chary Bonala

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Benoît Dejoncheere

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  1. Narasimha Chary Bonala
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  2. Benoît Dejoncheere
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Correspondence to Benoît Dejoncheere.

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Bonala, N.C., Dejoncheere, B. Cohomology of line bundles on horospherical varieties. Math. Z. 296, 525–540 (2020). https://doi.org/10.1007/s00209-019-02454-y

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