Hypersurfaces singular along a curve (Q765728)

Let \(C\) be a smooth irreducible curve of degree \(d\) and genus \(g\) in the projective space \(\mathbb{P}^r\). The paper gives sufficient conditions in the form of three inequalities involving \(n\), \(d\), \(g\), \(r\) and \(k\) for the existence of a hypersurface of degree \(n\) in \(\mathbb{P}^r\) vanishing of order \(k\) along \(C\).