Penrose, Roger; Smith, Cedric A. B. A quadratic mapping with invariant cubic curve. (English) Zbl 0453.14005 Math. Proc. Camb. Philos. Soc. 89, 89-105 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 3 Documents MSC: 14E07 Birational automorphisms, Cremona group and generalizations 14E05 Rational and birational maps 14M07 Low codimension problems in algebraic geometry 51A20 Configuration theorems in linear incidence geometry 92D10 Genetics and epigenetics Keywords:pencil of cubics; Pascal configuration; Cremona transformation; mathematical genetics; field of elliptic functions PDFBibTeX XMLCite \textit{R. Penrose} and \textit{C. A. B. Smith}, Math. Proc. Camb. Philos. Soc. 89, 89--105 (1981; Zbl 0453.14005) Full Text: DOI References: [1] Coxeter, Acta Arithmetica 28 pp 297– (1971) [2] Duval, Elliptic functions and elliptic curves (1973) · doi:10.1017/CBO9781107359901 [3] Burnside, Theory of groups of finite order (1911) · JFM 42.0151.02 [4] Baker, Principles of geometry 5 (1933) [5] Zeuthen, Lehrbuch der Abz?hlenden Methoden der Geometrie (1914) · JFM 45.0799.01 [6] Semple, Introduction to algebraic geometry (1949) · Zbl 0041.27903 [7] Segre, Atti dell’ Accademia delle Scienze, Torino 24 pp 734– (1889) [8] DOI: 10.1038/hdy.1959.52 · doi:10.1038/hdy.1959.52 [9] Neville, Elliptic functions, a primer (1971) · Zbl 0229.33004 · doi:10.1016/B978-0-08-016369-7.50022-8 [10] Neville, Jacobian elliptic functions (1954) · Zbl 0060.21404 [11] DOI: 10.1038/hdy.1959.36 · doi:10.1038/hdy.1959.36 [12] DOI: 10.2307/2309342 · Zbl 0094.00903 · doi:10.2307/2309342 [13] DOI: 10.2307/3609268 · doi:10.2307/3609268 [14] DOI: 10.2307/3606036 · doi:10.2307/3606036 [15] Komissaruk, Vy?ej?aja ?kola (1967) [16] Coxeter, Abh. Math. Sem., Univ. Hamburg 34 pp 38– (1969) 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.