On the fattening of lines in P3P3

We follow the lead of [2] and show how differences in the invariant α   can be used to classify certain classes of subschemes of P3P3. Specifically, we will seek to classify arithmetically Cohen–Macaulay codimension 2 subschemes of P3P3 in the manner Bocci and Chiantini classified points in P2P2. The first section will seek to motivate our consideration of the invariant α by relating it to the Hilbert function and γ, following the work of [2] and [5]. The second section will contain our results classifying arithmetically Cohen–Macaulay codimension 2 subschemes of P3P3. This work is adapted from the author's Ph.D. dissertation [11].