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- W4313646871 abstract "Abstract In this paper, we study the Koszul property of the homogeneous coordinate ring of a generic collection of lines in $mathbb {P}^n$ and the homogeneous coordinate ring of a collection of lines in general linear position in $mathbb {P}^n.$ We show that if $mathcal {M}$ is a collection of m lines in general linear position in $mathbb {P}^n$ with $2m leq n+1$ and R is the coordinate ring of $mathcal {M},$ then R is Koszul. Furthermore, if $mathcal {M}$ is a generic collection of m lines in $mathbb {P}^n$ and R is the coordinate ring of $mathcal {M}$ with m even and $m +1leq n$ or m is odd and $m +2leq n,$ then R is Koszul. Lastly, we show that if $mathcal {M}$ is a generic collection of m lines such that $$ begin{align*} m> frac{1}{72}left(3(n^2+10n+13)+sqrt{3(n-1)^3(3n+5)}right),end{align*} $$ then R is not Koszul. We give a complete characterization of the Koszul property of the coordinate ring of a generic collection of lines for $n leq 6$ or $m leq 6$ . We also determine the Castelnuovo–Mumford regularity of the coordinate ring for a generic collection of lines and the projective dimension of the coordinate ring of collection of lines in general linear position." @default.
- W4313646871 created "2023-01-07" @default.
- W4313646871 creator A5080104443 @default.
- W4313646871 date "2023-01-06" @default.
- W4313646871 modified "2023-09-27" @default.
- W4313646871 title "GENERIC LINES IN PROJECTIVE SPACE AND THE KOSZUL PROPERTY" @default.
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- W4313646871 doi "https://doi.org/10.1017/nmj.2022.42" @default.
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