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- W3042940072 abstract "The study of the defining equations of a finite set $Gamma subset mathbb{P}^n$ in linearly general position has been actively attracted since it plays a significant role in understanding the defining equations of arithmetically Cohen-Macaulay varieties. In cite{T}, R. Treger proved that $I(Gamma)$ is generated by forms of degree $leq lceil frac{|Gamma|}{n}rceil$. Since then, Treger's result have been extended and improved in several papers. The aim of this paper is to reprove and improve the above Treger's result from a new perspective. Our main result in this paper shows that $I(Gamma)$ is generated by the union of $I(Gamma)_{leq lceil frac{|Gamma|}{n}rceil -1}$ and the set of all completely decomposable forms of degree $lceil frac{|Gamma|}{n}rceil$ in $I(Gamma)$. In particular, it holds that if $d leq 2n$ then $I(Gamma)$ is generated by quadratic equations of rank $2$. This reproves Saint-Donat's results in cite{SD1} and cite{SD2}." @default.
- W3042940072 created "2020-07-23" @default.
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- W3042940072 date "2020-07-14" @default.
- W3042940072 modified "2023-09-27" @default.
- W3042940072 title "On completely decomposable defining equations of points in general position in Pn" @default.
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