论文标题
高度曲线的二次方程等级
On the rank of quadratic equations for curves of high degree
论文作者
论文摘要
令$ \ mathcal {c} \ subset \ mathbb {p}^r $为算术属$ g $和度$ d $的线性正常曲线。在\ cite {sd}中，B。Saint-Donat证明了$ \ Mathcal {C} $的均质理想$ i（\ Mathcal {C}）$，每当$ 4 $的排名中，每当$ 4 $时，每当$ d \ d \ d \ d \ d \ egeq 2g+2 $ 2 $。另外，在\ cite {eks} eisenbud，koh和Stillman证明$ i（\ mathcal {c}）$如果$ d \ geq 4g+2 $，则允许确定性呈现。在本文中，我们将证明$ i（\ Mathcal {c}）$可以由二次方程$ 3 $生成$ 3 $，如果$ g = 0,1 $和$ d \ geq 2g+2 $或$ g \ geq 2 $和$ d \ geq 2 $和$ d \ d \ geq 4g+4 $。
Let $\mathcal{C} \subset \mathbb{P}^r$ be a linearly normal curve of arithmetic genus $g$ and degree $d$. In \cite{SD}, B. Saint-Donat proved that the homogeneous ideal $I(\mathcal{C})$ of $\mathcal{C}$ is generated by quadratic equations of rank at most $4$ whenever $d \geq 2g+2$. Also, in \cite{EKS} Eisenbud, Koh and Stillman proved that $I(\mathcal{C})$ admits a determinantal presentation if $d \geq 4g+2$. In this paper, we will show that $I(\mathcal{C})$ can be generated by quadratic equations of rank $3$ if either $g=0,1$ and $d \geq 2g+2$ or else $g \geq 2$ and $d \geq 4g+4$.
