GENERIC LINES IN PROJECTIVE SPACE AND THE KOSZUL PROPERTY

Abstract In this paper, we study the Koszul property of homogeneous coordinate ring a generic collection lines in $\mathbb {P}^n$ and general linear position {P}^n.$ We show that if $\mathcal {M}$ is m with $2m \leq n+1$ R {M},$ then Koszul. Furthermore, even $m +1\leq n$ or odd +2\leq n,$ Lastly, such $$ \begin{align*} m> \frac{1}{72}\left(3(n^2+10n+13)+\sqrt{3(n-1)^3(3n+5)}\right),\end{align*} not give complete characterization for $n 6$ . also determine Castelnuovo–Mumford regularity projective dimension position.