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On the arithmetic genus of rational curves. (Sur le genre arithmétique des courbes rationnelles.) (French) Zbl 0854.14017
Summary: Harris and Eisenbud found a bound for the genus of curves of degree \(d\) in the projective space \(\mathbb{P}_r\) that are not contained in surfaces of degree less than \(s\) (with \(s<2r-2\)). We give elementary constructions of rational curves with a maximal arithmetic genus for \(s<2r-3\), that is with a maximal singular locus. Our curves have only real ordinary singular points with real tangents. When it is possible they are nodal curves.

14H50 Plane and space curves
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