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Algebraic Curves Given by Puiseux Tree

Publication at Faculty of Mathematics and Physics |
2017

Abstract

Puiseux tree represents locally planar curve branches at a given point. It is well known how to find Puiseux tree from the algebraic equation of the curve.

We consider the other direction and propose an algorithm to find algebraic equation of (one of many) curve having prescribed Puiseux tree or branches at the origin. It allows us to generate curves having singularities of given properties.