Nodal singular locus conjecture for projected complete intersection curves

Let $A\in\mathbb Z^{n+2}$ be a finite set of full dimension containing $0\in\mathbb Z^{n+2}$ and satisfying Assumption. For generic polynomials $f_1,\ldots,f_{n+1}\in\mathbb C^{A}$, let

$$\widetilde{\mathcal C}=\\{f_1=\cdots=f_{n+1}=0\\}\subset (\mathbb C\setminus 0)^{n+2}$$

be the complete intersection curve, and let

$$\pi\colon(\mathbb C\setminus 0)^{n+2}\to(\mathbb C\setminus 0)^2$$

be the projection forgetting the first $n$ coordinates. Nodal singular locus conjecture. The image $\pi(\widetilde{\mathcal C})$ is an algebraic plane curve with punctured points, and its singular locus consists only of nodes. This predicts that generic projected complete intersection curves have no singularities beyond ordinary double points, a property relevant to understanding the geometry and combinatorics of their plane projections; the conjecture is stated here as a further discussion and no resolution is supplied in the source.