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.
You have full access to this open access chapter, Download chapter PDF
Similar content being viewed by others
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.
References
Th. Bauer, G. Malara, T. Szemberg, J. Szpond, Quartic unexpected curves and surfaces. Manuscript Math. (to appear). arXiv:1804.03610
D. Cook II, B. Harbourne, J. Migliore, U. Nagel, Line arrangements and configurations of points with an unusual geometric property. Compos. Math. 154(10), 2150–2194 (2018)
M. Di Marca, G. Malara, A. Oneto, Unexpected curves arising from special line arrangements. J. Algebraic Combin. (to appear) arXiv:1804.02730
M. Dumnicki, Ł. Farnik, B. Harbourne, G. Malara, J. Szpond, H. Tutaj-Gasińska, A matrixwise approach to unexpected hypersurfaces (2019). Preprint. arXiv:1901.03725
Ł. Farnik, F. Galuppi, L. Sodomaco, W. Trok, On the unique unexpected quartic in \(\mathbb {P}^2\). J. Algebraic Combin. (to appear). arXiv:1804.03590
B. Harbourne, J. Migliore, U. Nagel, Z. Teitler, Unexpected hypersurfaces and where to find them. Mich. Math. J. (to appear). arXiv:1805.10626
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Carlini, E., Tài Hà, H., Harbourne, B., Van Tuyl, A. (2020). Final Comments and Further Reading. In: Ideals of Powers and Powers of Ideals. Lecture Notes of the Unione Matematica Italiana, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-030-45247-6_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-45247-6_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-45246-9
Online ISBN: 978-3-030-45247-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)