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Tropical Hopf manifolds and contracting germs

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Abstract

Classical Hopf manifolds are compact complex manifolds whose universal covering is \(\mathbb {C}^d \backslash \{0\}\). We investigate the tropical analogues of Hopf manifolds, and relate their geometry to tropical contracting germs. To do this we develop a procedure called monomialization which transforms non-degenerate tropical germs into morphisms, up to tropical modification. A link is provided between tropical Hopf manifolds and the analytification of Hopf manifolds over a non-archimedean field. We conclude by computing the tropical Picard group and (p, q)-homology groups.

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Authors and Affiliations

  1. IMJ, Université Paris 7, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    Matteo Ruggiero

  2. Technische Universität Berlin, MA 6-2, 10623, Berlin, Germany

    Kristin Shaw

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  1. Matteo Ruggiero
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  2. Kristin Shaw
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Correspondence to Kristin Shaw.

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Ruggiero, M., Shaw, K. Tropical Hopf manifolds and contracting germs. manuscripta math. 152, 1–60 (2017). https://doi.org/10.1007/s00229-016-0849-8

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