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Let $X$ be a smooth surface and let $\varphi:X\to\mathbb{P}^N$, with $N\geq4$, be a finitely ramified map which is birational onto its image $Y =\varphi(X)$, with $Y$ non-degenerate in $\mathbb{P}^N$. In this paper, weproduce a lower bound for the length of the pinch scheme of a general linearprojection of $Y$ to $\mathbb{P}^3.$ We then prove that the lower bound isrealized if and only if $Y$ is a rational normal scroll.

Bounding Pinch Point Schemes of Projected Surfaces