The number of reducible space curves over a finite field |
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| Authors: | Eda Cesaratto Joachim von zur Gathen Guillermo Matera |
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| Affiliation: | 1. Instituto del Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150 (B1613GSX), Los Polvorines, Buenos Aires, Argentina;2. National Council of Science and Technology (CONICET), Argentina;3. B-IT, Universität Bonn, D-53113 Bonn, Germany |
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| Abstract: | “Most” hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by the appropriate Chow variety, and provides bounds on the probability that a random curve over a finite field is reducible. |
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