MEGA 2007Effective Methods in Algebraic Geometry Strobl, Austria, June 25th - 29th |
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Electronic Proceedings
Abstract
| Title | Inherently Improper Parametric Supports for Unirational Varieties |
| Keywords | Inherently improper supports, improper rational parametrizations, support transformation, reparametrization, Chow form, lattice reduction, BKK bound. |
| Abstract | A class of parametric 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. For a generic rational parametrization defined on an inherently improper support, we prove that its improper index is the gcd of the normalized volumes of all the simplex sub-supports and give an algorithm to obtain a proper reparametrization. Properties of non-degenerate rational parametrizations defined on an inherently improper parametric support with coefficients from some subfield of $C$ are also considered. Finally, the coordinate and lattice structures of inherently improper parametric supports are analyzed and a reparametrization algorithm of better complexity is given. |
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