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Proper reparametrization for inherently improper unirational varieties

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Abstract

In this paper, a class of lattice supports in the lattice space Z m is found to be inherently improper because any rational parametrization from C m to C n defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.

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Authors and Affiliations

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing, 100049, China

    Liyong Shen

  2. School of Computing, National University of Singapore, 117543, Singapore, Singapore

    Engwee Chionh

  3. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiao-Shan Gao

  4. Beijing Electrical Science and Technology Institute, Beijing, 100070, China

    Jia Li

Authors
  1. Liyong Shen
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  2. Engwee Chionh
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  3. Xiao-Shan Gao
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  4. Jia Li
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Corresponding author

Correspondence to Liyong Shen.

Additional information

This research is supported by the National Key Basic Research Project of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 10901163.

This paper was recommended for publication by Editor Ziming LI.

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Shen, L., Chionh, E., Gao, XS. et al. Proper reparametrization for inherently improper unirational varieties. J Syst Sci Complex 24, 367–380 (2011). https://doi.org/10.1007/s11424-010-7221-y

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  • DOI: https://doi.org/10.1007/s11424-010-7221-y

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