Recent Remarks on Analytical Equivalence

Alberto de Azevedo

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 183-188 from Springer

Abstract: Abstract Let c be the conductor of a plane algebroid curve Γ, defined over an algebraically closed field of characteristic zero. This expository article describes, up to analytical equivalence, all such Γ whose jacobian ideal has length equal to c,c-1 or c−2. The case of length c was previously considered by O. Zariski [10], the further cases are recent work of Valmecir Bayer and Abramo Hefez [3]. This article also deals with counterexamples to a conjecture made by the author in 1967 [2]. The first counterexample was given by J. Heinrich ([4] and [7]) and recently M. Escudeiro [6] has thrown more light on the subject.

Date: 2004
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DOI: 10.1007/978-3-642-18487-1_9

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