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arxiv: 1307.1633 · v1 · pith:56WO7PZAnew · submitted 2013-07-05 · 🧮 math.NT · math.AG

The number of reducible space curves over a finite field

classification 🧮 math.NT math.AG
keywords fieldfinitereduciblespacecurvesprobabilityrandomappropriate
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"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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