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Other systems of invariants for the equisingularity of plane algebroid curves

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Part of the Lecture Notes in Mathematics book series (LNM,volume 813)

Abstract

In this chapter we consider new complete systems of invariants for the equiresolution of plane algebroid curves and their relationship with the characteristic exponents.

The first of them is explained in the first section and it is formed by the Newton coefficients given by Lejeune in (15). In the second section we study briefly the maximal contact of any genus, using Hamburger-Noether expansions. The third section is devoted to the semigroup of values of a plane curve. We compute it and obtain results analogous to those of the characteristic zero case. Finally in the fourth section we generalize to the case of positive characteristic the main properties of the degree of the conductor of any curve.

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© 1980 Springer-Verlag

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Campillo, A. (1980). Other systems of invariants for the equisingularity of plane algebroid curves. In: Algebroid Curves in Positive Characteristic. Lecture Notes in Mathematics, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090827

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  • DOI: https://doi.org/10.1007/BFb0090827

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10022-5

  • Online ISBN: 978-3-540-38178-5

  • eBook Packages: Springer Book Archive