  In this notes we study complex projective plane curves whose graded module of
Jacobian syzygies is generated by its minimal degree component. Examples of
such curves include the smooth curves as well as the maximal Tjurina curves.
However, this class of curves seems to be surprisingly large. In particular,
any line arrangement $\mathcal A$ of $d=2k+1\geq 5 $ lines having only double
and triple points is in this class if the number of triple points is $k$ and if
they are all situated on a line $L \in \mathcal A$, see Theorem 6.2
