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Seminar on Algebraic Geometry

Tuesday, 11.1., 15:00 - 16:30
ricam seminar room

Josef Schicho
Level and Keel

The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. We introduce two numerical invariants of a rational surface, called level and keel. These two numbers govern the parametric degree in the sense that there exist linear upper and lower bounds. It cannot be expected that level and keel determine the parametric degree exactly, because these invariants do not change under extension of the base field, but the parametric degree depends on the base field.