Abstract
One year after Clebsch’s paper [45], Cayley published an article which cites it, but without retaining the term “genus” suggested by Clebsch. Cayley introduced a rival term, the “deficiency” . This term was used for more or less half a century, mainly by British mathematicians, before being abandoned in favor of “genus”. Here is the way in which Cayley explained the reason behind his choice (see [38, pp. 1–2])
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Notes
- 1.
This theorem states that the number of intersection points, counted with multiplicities, of two complex plane projective curves without common components, is equal to the product of their degrees.
References
A. Cayley, On the Transformation of Plane Curves. Proc. Lond. Math. Soc. 1 (III), 1–11 (1865/1866)
A. Clebsch, Ueber diejenigen ebenen Curven, deren Coordinaten rationale Functionen eines Parameters sind. J. Reine Angew. Math. 64, 43–65 (1865)
O. Labs, Hypersurfaces with many singularities – history, constructions, algorithms, visualization. Thesis, University of Mainz, 2005
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Popescu-Pampu, P. (2016). Cayley and the Deficiency. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_21
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DOI: https://doi.org/10.1007/978-3-319-42312-8_21
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