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arXiv · 2502.19509

Geometric deformations of implicit curves

Marco Antônio do Couto Fernandes·Samuel Paulino dos Santos
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Abstract

Let f = 0 be an implicit singular plane curve. When deforming f = 0, inflections and vertex emerge from the singularities. In this papper, we classify the deformations of f = 0 with respect to the inflections and the vertices in the cases of codimension less than or equal to 2, that is, in the cases that occur generically in families of implicit curves with 2 parameters.

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Marco Antônio do Couto Fernandes, Samuel Paulino dos Santos. 2025-02-26. Geometric deformations of implicit curves. https://arxiv.org/abs/2502.19509

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