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Reconstructing birational maps from their face functions

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Abstract

We first prove that any birational map, from an affine space of dimension ≥ 2 to itself, is not determined by its face functions. On the other hand, we prove that a birational map with irreducibly polynomial inverse is completely determined, within the class of all birational maps with irreducibly polynomial inverses, by its face functions. We show also how to effectively reconstruct such a map from its face functions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, H3A 2K6, Montreal, Quebec, Canada

    Wei Li

  2. Department of Mathematics, University of Notre Dame, 46556, Notre Dame, IN, USA

    Jie-Tai Yu

Authors
  1. Wei Li
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  2. Jie-Tai Yu
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Supported partly by the Centre Interuniversitaireen Calcul Mathématique Algébrique.

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Li, W., Yu, JT. Reconstructing birational maps from their face functions. Manuscripta Math 76, 353–366 (1992). https://doi.org/10.1007/BF02567766

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  • DOI: https://doi.org/10.1007/BF02567766

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