The number of reducible space curves over a finite field

Eda Cesaratto; Joachim von zur Gathen; Guillermo Matera

doi:10.1016/j.jnt.2012.08.027

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arXiv · 1307.1633

The number of reducible space curves over a finite field

Eda Cesaratto·Joachim von zur Gathen·Guillermo Matera

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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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Eda Cesaratto, Joachim von zur Gathen, Guillermo Matera. 2013-07-05. The number of reducible space curves over a finite field. https://doi.org/10.1016/j.jnt.2012.08.027

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