a subvariety of dimension $\dfrac{d(d+1)}{2}-1$, and all we have to do is check if $(d-1)d > \dfrac{d(d+1)}{2}-1$, which is obvious if $d \ge 3$ (we remark that there are not two different curves of degree $d-1$ passing through the $(d-1)d$ points $P_1^{\prime},\dots,P_l^{\prime}$). We select then $P_1^{\prime},\dots,P_l^{\prime}$ outside this subvariety in order to get the ramification map $f$ and take a lifting $F$ defined in a surface $S$. We prove then the statement: there is no embedding $\Phi: S\rightarrow {\mathbb P^2}$. In fact, the submersion $F\circ{\Phi^{-1}}$ defined in a neighborhood of $C_0 \subset {\mathbb P^2}$ extends to $\mathbb P^2$ as a meromorphic function (holomorphic in a neighborhood of $C_0$). We observe that, for $d\ge 3$, given two embeddings $\phi_i:C\rightarrow {\mathbb P^2}$, i=1,2 there exists an automorphism $T\in Aut(\mathbb P^2)$ such that $T(\phi_1(C))= \phi_2(C)$, see Appendix. Then the map $\Phi|_{C}:C \rightarrow C_0$ comes from a linear map on $\Pp^2$ and poles of $f$ are the intersection of $C$ with a curve of degree $d-1$, which is impossible.

We present now an example of a non embeddable pair (curve, surface) with a set of two fibrations which is projective at the curve. We start with a projective, smooth curve $C$ and select two 