The Analytic Classification of Plane Curves
Marcelo Escudeiro Hernandes, Maria Elenice Rodrigues Hernandes
TL;DR
This paper provides an algebraic method for the analytic classification of germs of plane curves with multiple components, building on and extending previous work by Zariski.
Contribution
It introduces a new algebraic approach to classify plane curve germs analytically, recovering some known cases and offering a systematic solution.
Findings
Algebraic classification method for plane curve germs.
Extension of Zariski's ideas to multiple components.
Recovery of specific cases from existing literature.
Abstract
In this paper, we present a solution to the problem of the analytic classification of germs of plane curves with several irreducible components. Our algebraic approach follows precursive ideas of Oscar Zariski and as a subproduct allow us to recover some particular cases found in the literature.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Mathematics and Applications · Polynomial and algebraic computation