Abstract
In this chapter we turn our attention to double points in \(\mathbb{P}^{1} \times \mathbb{P}^{1}\), that is, sets of fat points where every point has multiplicity two. Using our classification of ACM sets of fat points in \(\mathbb{P}^{1} \times \mathbb{P}^{1}\) that we developed in the previous chapter, it is not difficult to show that these sets of points are rarely ACM. In fact, even if the support of the set of fat points is ACM, it is not even true that the set of double points supported on this set of points is ACM as seen in Example 6.23.
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Guardo, E., Van Tuyl, A. (2015). Double points and their resolution. In: Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-24166-1_7
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DOI: https://doi.org/10.1007/978-3-319-24166-1_7
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