Obstructions to Deforming Space Curves and Non-reduced Components of the Hilbert Scheme
Obstructions to Deforming Space Curves and Non-reduced Components of the Hilbert Scheme
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DOI：
10.2977/prims/1166642061
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发表时间：
2005-05
影响因子：
1.2
通讯作者：
Hirokazu Nasu
中科院分区：
文献类型：
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作者：
Hirokazu Nasu
设hssp3表示P3中光滑连通曲线的希尔伯特格式。我们考虑极大不可约闭子集W∧H S3，其一般元素C包含在光滑三次曲面上，并研究W是（H S3）红的一个分量的条件。我们特别研究了H S P3在[C]处的切空间的维数比暗淡W（≥4d eg(C)）大1的情况。我们计算了P3中C变形的障碍，并证明了在这种情况下，对于每一个W， hs3沿着W是不约简的，并且W是（hs3 P3）红的一个分量。
Let H S P3 denote the Hilbert scheme of smooth connected curves in P 3 .W e consider maximal irreducible closed subsets W ⊂ H S3 whose general member C is contained in a smooth cubic surface and investigate the conditions for W to be a component of (H S3 )red. We especially study the case where the dimension of the tangent space of H S P3 at [C] is greater than dim W (≥ 4d eg(C)) by one. We compute obstructions to deforming C in P 3 and prove that for every W in this case, H S3 is non-reduced along W and W is a component of (H S P3 )red.