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Puiseux and the Permutations of Roots

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Part of the Lecture Notes in Mathematics book series (HISTORYMS,volume 2162)

Abstract

As was explained by Cauchy in the excerpt of the paper [37] discussed in the previous chapter, if one takes a path which comes back to its starting point

Keywords

  • Fractional Power Series
  • Loop Elements
  • Newton-Puiseux Series
  • Local Irreducible Components
  • Brieskorn

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Fig. 13.1

Notes

  1. 1.

    This may always be arranged by the so-called Weierstrass preparation theorem (see [25]).

References

  1. E. Brieskorn, H. Knörrer, Plane Algebraic Curves (Birkhäuser Verlag, Boston, 1986). Translation by J. Stillwell of the first German edition of 1981

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  2. A.L. Cauchy, Considérations nouvelles sur les intégrales définies qui s’étendent à tous les points d’une courbe fermée, et sur celles qui sont prises entre des limites imaginaires. C.R. Acad. Sci. Paris 23, 689–702 (1846).

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  3. G. Fischer, Plane Algebraic Curves. Student Mathematical Library, vol. 15 (American Mathematical Society, Providence, RI, 2001). Translated from the 1994 German original by L. Kay

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  4. V. Puiseux, Recherches sur les fonctions algébriques. J. Math. Pures Appl. (Journ. de Liouville) 15, 365–480 (1850)

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  5. C.T.C. Wall, Singular Points of Plane Curves. London Mathematical Society Student Texts, vol. 63 (Cambridge University Press, Cambridge, 2004)

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Popescu-Pampu, P. (2016). Puiseux and the Permutations of Roots. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_13

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