## Moduli of germs of Legendrian curves.(English)Zbl 1187.14004

Legendrian curves (in $$3$$–space) are studied. The equisingularity type of a germ of Legendrian curve is (by definition) the topological type of its generic plane projection. If $$C$$ is the germ at the origin of a singular irreducible plane curve parametrized by $$x=t^n, y=\sum_{i=m}^\infty a_it^i$$ then the conormal $$\Lambda$$ of the curve is parametrized by $$x=t^n, y=\sum_{i=m}^\infty a_i t^i$$, $$p=\frac{dy}{dx}\cdot\sum_{i=m}^\infty\frac{i}{n}a_it^i$$. This is an example for a Legendrian curve.
The generic component of the moduli space of the germs of Legendrian curves with generic plane projection topological equivalent to a curve $$y^n=x^m$$ is constructed.

### MSC:

 14B05 Singularities in algebraic geometry 32S05 Local complex singularities 14D22 Fine and coarse moduli spaces

### Keywords:

singularities of curves; moduli space; Legendrian curve
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### References:

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