在二次曲面内变形规范曲线
Deforming a canonical curve inside a quadric
摘要：
设$C\subset{\mathbb P}^{g-1}$是亏格为$g$的正则嵌入非奇异非超椭圆曲线，$X\subset{\mathbb P}^{g-1}$是包含$C$的二次曲面.我们的主要结果指出，除其他事项外，希尔伯特计划的$X$是在$[C\subset X]$的一个局部完全相交的维度$g^2-1$，是光滑的，当$X$。它还包括这样的断言，即该变形问题的最小障碍空间实际上是完全相关的$\operatorname{Ext}^1$ -群，并且特别是在$C$满足$X$的奇异轨迹的情况下，$X$中的$C$的变形被障碍。正如我们将在即将发表的论文中展示的那样，这具有拓扑性质的应用。
英文摘要：
Let $C\subset{\mathbb P}^{g-1}$ be a canonically embedded nonsingular nonhyperelliptic curve of genus $g$ and let $X\subset{\mathbb P}^{g-1}$ be a quadric containing $C$. Our main result states among other things that the Hilbert scheme of $X$ is at $[C\subset X]$ a local complete intersection of dimension $g^2-1$, and is smooth when $X$ is. It also includes the assertion that the minimal obstruction space for this deformation problem is in fact the full associated $\operatorname{Ext}^1$-group and that in particular the deformations of $C$ in $X$ are obstructed in case $C$ meets the singular locus of $X$. As we will show in a forthcoming paper, this has applications of a topological nature.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
