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Title: Proper reparametrization for inherently improper unirational varieties
Authors: Shen, L.
Chionh, E. 
Gao, X.-S.
Li, J.
Keywords: BKK bound
chow form
improper lattice supports
improper rational parametrizations
support transformation
Issue Date: 2011
Citation: Shen, L., Chionh, E., Gao, X.-S., Li, J. (2011). Proper reparametrization for inherently improper unirational varieties. Journal of Systems Science and Complexity 24 (2) : 367-380. ScholarBank@NUS Repository.
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. © 2011 Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg.
Source Title: Journal of Systems Science and Complexity
ISSN: 10096124
DOI: 10.1007/s11424-010-7221-y
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