Ballico, Edoardo; Oliverio, Paolo Nodal curves in \(\mathbb{P}^3(\mathbb{C})\). (English) Zbl 0607.14019 Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 76, 253-259 (1984). Here we prove the following result: For all integers \((d,g)\) such that there is a smooth connected curve in \({\mathbb{P}}^ 3\) of genus \(g\) and degree \(d,\) and every t with \(0\leq t\leq g\), there is an irreducible curve \(C\subset {\mathbb{P}}^ 3\) of arithmetic genus \(g,\) degree \(d,\) with exactly \(t\) nodes as only singularities. - The proof uses Severi-Wahl-Tannenbaum’s theory of nodal curves on rational surfaces, and the proof by Gruson-Peskine of Halphen’s conjecture about the possible \((d,g)\) for smooth curves in \({\mathbb{P}}^ 3\). Cited in 1 Document MSC: 14H20 Singularities of curves, local rings 14N05 Projective techniques in algebraic geometry Keywords:degree; arithmetic genus; nodal curves on rational surfaces; Halphen’s conjecture; smooth curves PDFBibTeX XMLCite \textit{E. Ballico} and \textit{P. Oliverio}, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 76, 253--259 (1984; Zbl 0607.14019)