The Hilbert Scheme of Space Curves of Degree d and Genus 3d−18
The Hilbert Scheme of Space Curves of Degree d and Genus 3d−18
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d 次属 3d−18 空间曲线的希尔伯特方案
DOI：
10.1080/00927870802175089
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发表时间：
2008
影响因子：
0.7
通讯作者：
Hirokazu Nasu
中科院分区：
文献类型：
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作者：
Hirokazu Nasu
记射影三维空间中亏格为g的d次光滑连通曲线的Hilbert概型。我们描述了对于任意整数d ≤ 16的所有不可约分支V。对于每个分量V，我们计算V的维数，并确定是否沿沿着V一般光滑。证明了当d ≥ 91时，则有唯一不可约分支，其一般成员包含在光滑三次曲面中，沿着是一般光滑的.
Let denote the Hilbert scheme of smooth connected curves of degree d and genus g in the projective 3-space ℙ3. We describe all irreducible components V of for every integer d ≤ 16. For each component V, we compute the dimension of V and determine whether is generically smooth along V or not. We show that if d ≥ 91, then has a unique irreducible component whose general member is contained in a smooth cubic surface, along which is generically smooth.