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On a certain generalization of triangle singularities

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Abstract

Triangle singularities are Fuchsian singularities associated with von Dyck groups, which are index two subgroups of Schwarz triangle groups. Hypersurface triangle singularities are classified by Dolgachev, and give 14 exceptional unimodal singularities classified by Arnold. We introduce a generalization of triangle singularities to higher dimensions, show that there are only finitely many hypersurface singularities of this type in each dimension, and give a complete list in dimension 3.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Kenji Hashimoto & Kazushi Ueda

  2. Department of Mathematics, University of California, Riverside, 900 University Ave, Riverside, CA, 92521, USA

    Hwayoung Lee

Authors
  1. Kenji Hashimoto
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  2. Hwayoung Lee
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  3. Kazushi Ueda
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Correspondence to Kazushi Ueda.

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Hashimoto, K., Lee, H. & Ueda, K. On a certain generalization of triangle singularities. manuscripta math. 153, 35–51 (2017). https://doi.org/10.1007/s00229-016-0876-5

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  • DOI: https://doi.org/10.1007/s00229-016-0876-5

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