关于$\mathbf{P}^3$品系的育肥
On the Fattening of Lines in $\mathbf{P}^3$
摘要：
我们遵循博奇和基安蒂尼的思路，展示了如何利用不变α的差异来对P^3的某些类别的子概型进行分类。具体地说，我们将试图以Bocci和Chiantini分类P^2中点的方式来分类P^3的算术Cohen-Macaulay余维2子概型。第一节将寻求激励我们考虑的不变阿尔法有关的希尔伯特函数和伽玛，以下工作的博奇和Chiantini，和Dumnicki等。第二部分将包含我们对P^3的算术Cohen-Macaulay余维2子概型进行分类的结果。这部作品改编自作者的博士学位。论文
英文摘要：
We follow the lead of Bocci and Chiantini and show how differences in the invariant alpha can be used to classify certain classes of subschemes of P^3. Specifically, we will seek to classify arithmetically Cohen-Macaulay codimension 2 subschemes of P^3 in the manner Bocci and Chiantini classified points in P^2. The first section will seek to motivate our consideration of the invariant alpha by relating it to the Hilbert function and gamma, following the work of Bocci and Chiantini, and Dumnicki, et. al. The second section will contain our results classifying arithmetically Cohen-Macaulay codimension 2 subschemes of P^3. This work is adapted from the author's Ph.D. dissertation.
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