10次点集Hilbert概型的Gorenstein轨迹的不可约性
Irreducibility of the Gorenstein locus of the punctual Hilbert scheme of degree 10
摘要：
设$k$是特征为0的代数闭域，$H_G(d,N)$是Hilbert概型$H(d,N)$在射影N-空间中对应于$d$次Gorenstein子概型的开轨迹.我们在以前的文章中证明了$H_G(d,N)$对于$d\le9$和$N\ge1$是不可约的。本文证明了对于每个$N\ge1$，$H_G(10,N)$也是不可约的，并给出了其奇异轨迹的完整描述.
英文摘要：
Let $k$ be an algebraically closed field of characteristic 0 and let $H_G(d,N)$ be the open locus of the Hilbert scheme $H(d,N)$ corresponding to Gorenstein subschemes of degree $d$ in the projective N-space. We proved in a previous paper that $H_G(d,N)$ is irreducible for $d\le9$ and $N\ge1$. In the present paper we prove that also $H_G(10,N)$ is irreducible for each $N\ge1$, giving also a complete description of its singular locus.
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