On set theoretic complete intersections in \({\mathbb{P}}^ 3\) (Q1112900)

Let \(S\subset {\mathbb{C}}{\mathbb{P}}^ 3\) be a surface satisfying one of the following conditions: either it has at most ordinary nodes as singularities, or it has degree at most three, or it is a cone. Let \(D\subset S\) be a smooth curve. Assume that there exists another surface T such that \(D=S\cap T\) as sets. Under these conditions, we prove that degree\((D)\leq genus\)(D)\(+3\).