Where can the Castelnuovo-Mumford regularity of a projective curve be obtained? (Q2759230)

Let \(C\subseteq \mathbb{P}^n\) be a projective curve defined by a homogeneous ideal \(I\) with a minimal graded free resolutionNEWLINENEWLINE\[NEWLINE0\to \bigoplus^{\beta_p}_{j=1} S(-e_{pj}) @>\varphi_p>> \cdots @>\varphi_1>> \bigoplus^{\beta_0}_{j=1}S(-e_{0j}) @>\varphi_0>> I\to 0.NEWLINE\]NEWLINE NEWLINESetting \(e_i:=\max\{e_{ij};\;1\leq j\leq\beta_i\}\), the Castelnuovo-Mumford regularity is defined as \(\text{reg} (I):= \max \{e_i-i;\;0\leq i\leq p\}\). The author shows that it can be determined from the last two places, namelyNEWLINE\(\text{reg} (I) =\max \{e_{n-2}-n+2,e_{n-1}-n+1\}\).NEWLINENEWLINEFor the entire collection see [Zbl 0974.00043].