The number of reducible space curves over a finite field

Eda Cesaratto, Joachim von zur Gathen, Guillermo Matera

Published 2013-07-05Version 1

"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.