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The parametric degree of a rational surface

Josef Schicho
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Abstract

The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. An example shows that the parametric degree is not a geometric but an arithmetic concept, in the sense that it depends on the choice of the ground field. In this paper, we introduce two geometrical invariants of a rational surface, namely level and keel. These two numbers govern the parametric degree in the sense that there exist linear upper and lower bounds.

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Josef Schicho. 2005-06-06. The parametric degree of a rational surface. https://arxiv.org/abs/math/0506097

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