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Geometry of Puiseux expansions

Geometry of Puiseux expansions

We consider the space $\mathrm{Curv}$ of complex affine lines $% t\mapsto(x,y)=(\phi(t),\psi(t))$ with monic polynomials $\phi$, $\psi$ of fixed degrees and a map $\mathrm{Expan}$ from $\mathrm{Curv}$ to a complex affine space $\mathrm{Puis}$ with $\dim\m