Gaps for the genera of multiple structures on projective curves (Q1921898)

In this paper one studies the gaps for the arithmetic genera of locally Cohen-Macaulay curves \(X\) in \(\mathbb{P}^r\), with the property that \(X_{\text{red}} = C\) are smooth curves and which are embedded in the first infinitesimal neighbourhood of \(C\) in \(\mathbb{P}^r\), in terms of \(d= \deg C\), \(r\), and the multiplicity of \(X\).