Pecker, Daniel Simple constructions of algebraic curves with nodes. (English) Zbl 0783.14013 Compos. Math. 87, No. 1, 1-4 (1993). The author gives a proof of the following results: There exists an integral nondegenerate (i.e. lying in no hyperplane) curve of degre \(d \geq n\) in \(\mathbb{P}^ n\), with \(\delta\) real nodes and no other singular points, for all \(\delta\) from 0 to the Castelnuovo’s bound. Over the field of complex numbers, this result was proved by Severi in the case \(n=2\); the case \(n \geq 3\) was proved by A. Tannenbaum [Math. Ann. 240, 213-221 (1979; Zbl 0385.14008) and Compos. Math. 41, 107-126 (1980; Zbl 0399.14018)], by using deformation theory. In the paper under review the author uses a method based on the simplification of nodes of certain Lissajous’s curves, following a technique described in a previous paper [C. R. Acad. Sci., Paris, Sér. I 315, No. 5, 561-565 (1992; see the preceding review)]. Reviewer: C.Cumino (Torino) Cited in 3 ReviewsCited in 8 Documents MSC: 14H20 Singularities of curves, local rings 14H50 Plane and space curves Keywords:real nodes; Castelnuovo’s bound; Lissajous’s curves Citations:Zbl 0392.14005; Zbl 0423.14015; Zbl 0783.14012; Zbl 0385.14008; Zbl 0399.14018 PDFBibTeX XMLCite \textit{D. Pecker}, Compos. Math. 87, No. 1, 1--4 (1993; Zbl 0783.14013) Full Text: Numdam EuDML References: [1] R. Benedetti , J.-J. Risler : Real algebraic and semi-algebraic sets . Actualités Mathématiques (1990). · Zbl 0694.14006 [2] D. Pecker : Courbes gauches ayant beaucoup de points multiples réels , to appear. · Zbl 0783.14012 [3] E.I. Shustin : Real Plane Algebraic Curves with Many Singularities . Preprint Samara State University, 1991. · Zbl 0786.14035 [4] A. Tannenbaum : Families of algebraic curves with nodes , Compositio Mathematica 41 (1980), 107-126. · Zbl 0399.14018 [5] A. Tannenbaum : On the geometric genera of projective curves , Math. Ann. 240(3) (1979), 213-221. · Zbl 0385.14008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.