The number of reducible space curves over a finite field

TL;DR

This paper investigates the likelihood of reducibility among space curves over finite fields by analyzing their parametrization via Chow varieties, providing bounds on the probability of reducibility.

Contribution

It introduces bounds on the probability that a random space curve over a finite field is reducible, using the Chow variety parametrization.

Findings

Bounds on reducibility probability for space curves over finite fields

Analysis of parametrization via Chow varieties

Extension of irreducibility estimates to space curves

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.