This paper deals with some classical problems about the projective geometry of complex algebraic curves. We call textit{locally toric} a projective curve that in a neighbourhood of every point has a local analytical parametrization of type $(t^{a_1},...,t^{a_n})$, with $a_1,..., a_n$ relatively prime positive integers. In this paper we prove that the general tangent line to a locally toric curve in $bP^3$ meets the curve only at the point of tangency. This result extends and simplifies those of the paper cite{kaji} by H.Kaji where the same result is proven for any curve in $bP^3$ such that every branch is smooth. More generally, under mild hypotesis, up to a finite number of anomalous parametrizations $(t^{a_1},...,t^{a_n})$, the general osculating 2-space to a locally toric curve of genus $g<2$ in $bP^4$ does not meet the curve again. The arithmetic part of the proof of this result relies on the Appendix cite{cz:rk} to this paper. By means of the same methods we give some applications and we propose possible further developments.
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