Final Comments and Further Reading

Abstract

The papers (Cook II et al., Compos Math 154(10):2150–2194, 2018; Harbourne et al., Mich Math J (to appear). arXiv:1805.10626) are essential reading for this section. The references in these papers give additional papers that may be useful to look at. This research topic is very new but of growing interest, so there are a lot of possible unexplored directions to take.

The papers [43, 101] are essential reading for this section; see also [11] and [60]. The references in these papers give additional papers that may be useful to look at. This research topic is very new but of growing interest, so there are a lot of possible unexplored directions to take.

Two such directions have been taken by two PRAGMATIC work groups. The results of these groups are written up in [54] and [72]. The paper [54] classifies all examples of point sets $Z\subset {\mathbb P}^2$ which have unexpected curves of degree t = m + 1 with a general fat singular point X = mp, under the assumption that the lines dual to the points of Z comprise what is known as a supersolvable line arrangement. The paper [72] shows that the 9 point set Z in Fig. 13.1 is the only one giving an unexpected quartic with a general point of multiplicity 3.