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arXiv · 2405.13958

Constructive solution of Zariski's Moduli Problem for Plane Branches

Pedro Fortuny Ayuso·Javier Ribón
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Abstract

In this paper we give an explicit solution to Zariski's moduli problem for plane branches. We compute (in an algorithmic way) the set of K\"{a}hler differentials of an irreducible germ of holomorphic plane curve. We show that there is a basis of this set whose main elements correspond to dicritical foliations. Indeed, we discuss several concepts of generation for the semimodule of values of K\"{a}hler differentials of the curve and provide basis of K\"{a}hler differentials, for every of these concepts, whose geometric properties are described. Moreover, we give an algorithmic construction of the bases.

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Pedro Fortuny Ayuso, Javier Ribón. 2024-05-22. Constructive solution of Zariski's Moduli Problem for Plane Branches. https://arxiv.org/abs/2405.13958

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