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Embeddings of \({\mathbb{C}^*}\)-surfaces into weighted projective spaces

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Abstract

Let V be a normal affine surface which admits \({\mathbb{C}^*}\) - and \({\mathbb{C}_+}\) -actions. Such surfaces were classified e.g., in: Flenner and Zaidenberg (Osaka J Math 40:981–1009, 2003; 42:931–974), see also the references therein. In this note we show that in many cases V can be embedded as a principal Zariski open subset into a hypersurface of a weighted projective space. In particular, we recover a result of D. Daigle and P. Russell, see Theorem A in: Daigle and Russell (Can J Math 56:1145–1189, 2004)

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Geb. NA 2/72, 44780, Bochum, Germany

    Hubert Flenner

  2. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Shulim Kaliman

  3. Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, BP 74, 38402, Saint-Martin-d’Hères Cedex, France

    Mikhail Zaidenberg

Authors
  1. Hubert Flenner
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  2. Shulim Kaliman
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  3. Mikhail Zaidenberg
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Correspondence to Mikhail Zaidenberg.

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Flenner, H., Kaliman, S. & Zaidenberg, M. Embeddings of \({\mathbb{C}^*}\)-surfaces into weighted projective spaces. manuscripta math. 131, 265–274 (2010). https://doi.org/10.1007/s00229-009-0315-y

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  • DOI: https://doi.org/10.1007/s00229-009-0315-y

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