On the Bourbaki Degree of Plane Projective Curves

Let $F$ be a reduced plane projective curve defined over an algebraically closed field $k$. The Bourbaki degree of $F$, denoted by $\mathrm{Bour}(F)$, measures its freeness and was introduced in \cite{JNS2024}. It is defined as the degree of $R/I_ε$, where $R = k[x,y,z]$ and $I_ε\subseteq R$ is the