No rational nonsingular quartic curve \({\mathcal C}_ 4\subset {\mathbb{P}}^ 3\) can be set-theoretic complete intersection on a cubic surface
Generalizing a result of \textit{E. Stagnaro} [Rend. Accad. Naz. Sci. Detta XL, V. Ser. Mem. Mat. 7, No.1, 51-87 (1983; Zbl 0545.14025)], the authors show that smooth rational quartic curves in \({\mathbb{P}}_ k^ 3\) (k algebraically closed of \(char(k)=0)\) are never set-theoretic complete intersections of any pairs of surfaces \(F_ 3\) and \(F_ n\), for every degree n.
scientific article; zbMATH DE number 4158826
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