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.


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