论文标题
6度的椭圆形曲线的几何形状
Geometry of elliptic normal curves of degree 6
论文作者
论文摘要
在我们的工作中，我们专注于嵌入在$ \ mathbb {p}^5 $中的椭圆形正常曲线的几何形状。我们通过6度的椭圆形正常曲线确定了二次超曲面的空间，并找到$ i（\ text {sec}（c_6））$的发电机的显式方程。我们在投影下从\ Mathbb {p}^5 $中的一般点$ p \和一般行$ \ overline {pq} \ subset \ subset \ mathbb {p}^5 $中研究图像$ c_p $和$ c_p $和$ c_p $和$ c_p $和$ c_p $和$ c_p $和$ c_p $和$ c_p $ c_6 $。特别是，我们表明$ c_p $是所有$ k $ j \ geq 2 $和$ i（c_p）$的$ k $ - $ c_p $由三个均质的多项式2均为2级的多项式生成，并且两个均质的多项式为3。由第3级和三个均质的多项式的两个均质多项式产生。
In our work we focus on the geometry of elliptic normal curves of degree 6 embedded in $\mathbb{P}^5$. We determine the space of quadric hypersurfaces through an elliptic normal curve of degree 6 and find the explicit equations of generators of $I(\text{Sec}(C_6))$. We study the images $C_p$ and $C_{pq}$ of a sextic $C_6$ under the projection from a general point $P \in \mathbb{P}^5$ and a general line $\overline{PQ} \subset \mathbb{P}^5$. In particular, we show that $C_p$ is $k$-normal for all $k \geq 2$ and $I(C_p)$ is generated by three homogeneous polynomials of degree 2 and two homogeneous polynomials of degree 3. We then show that $C_{pq}$ is $k$-normal for all $k \geq 3$ and $I(C_{pq})$ is generated by two homogeneous polynomials of degree 3 and three homogeneous polynomials of degree 4.
