标题： 关于高维射影空间中曲线的Hilbert概形 显示英文标题

标题： On the Hilbert scheme of curves in higher-dimensional projective space

摘要： In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(\P^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type. 显示英文摘要

摘要： In this paper we prove that, for any $n\ge 3$, there exist infinitely many $r\in \N$ and for each of them a smooth, connected curve $C_r$ in $\P^r$ such that $C_r$ lies on exactly $n$ irreducible components of the Hilbert scheme $\hilb(\P^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.