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Recent Remarks on Analytical Equivalence

In: Algebra, Arithmetic and Geometry with Applications

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  • Alberto de Azevedo

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.

Suggested Citation

  • Alberto de Azevedo, 2004. "Recent Remarks on Analytical Equivalence," Springer Books, in: Chris Christensen & Avinash Sathaye & Ganesh Sundaram & Chandrajit Bajaj (ed.), Algebra, Arithmetic and Geometry with Applications, pages 183-188, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18487-1_9
    DOI: 10.1007/978-3-642-18487-1_9
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