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LVMB manifolds and quotients of toric varieties

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Abstract

In this article we study a class of manifolds introduced by Bosio called \(\mathrm{{LVMB}}\) manifolds. We provide an interpretation of his construction in terms of quotient of toric manifolds by complex Lie groups. Furthermore, \(\mathrm{{LVMB}}\) manifolds extend a class of manifolds obtained by Meersseman, called \(\mathrm{{LVM}}\) manifolds and we give a characterization of these manifolds using our toric description. Finally, we give an answer to a question asked by Cupit-Foutou and Zaffran.

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Notes

  1. In the following we always, for short, say “cone” for a convex polyhedral cone with apex at the origin, since we will only consider such sets.

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Acknowledgments

I would like to thank my thesis advisor Karl Oeljeklaus for his constant support, helpful discussions and comments, as well as Dan Zaffran for interesting conversations and suggestions on the topic. I also wish to thank Jean-Jacques Loeb, Laurent Meersseman and the unknown referee for detailed reading of the paper and useful remarks. Finally thanks go to Saurabh Trivedi for friendly encouragement.

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  1. Laboratoire d’Analyse, Topologie, Probabilités, UMR CNRS 7353, Université d’Aix-Marseille, 39 Rue F. Joliot-Curie, 13013 , Marseille, France

    L. Battisti

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  1. L. Battisti
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Correspondence to L. Battisti.

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Financial support for this PhD thesis is assured by the French Région Provence-Alpes-Côte d’Azur

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Battisti, L. LVMB manifolds and quotients of toric varieties. Math. Z. 275, 549–568 (2013). https://doi.org/10.1007/s00209-013-1147-8

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