Abstract
Our research is motivated by recent work of Cook II, Harbourne, Migliore, and Nagel on configurations of points in the projective plane with properties that are unexpected from the point of view of the postulation theory. In this note, we revisit the basic configuration of nine points appearing in work of Di Gennaro/Ilardi/Vallès and Harbourne, and we exhibit some additional new properties of this configuration. We then pass to projective three-space \(\mathbb {P}^3\) and exhibit a surface with unexpected postulation properties there. Such higher dimensional phenomena have not been observed so far.
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Acknowledgements
This research has been initiated while the three last authors visited the University of Marburg. It is a pleasure to thank the Department of Mathematics in Marburg for hospitality and István Heckenberger and Volkmar Welker for helpful conversations.
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The research of the Grzegorz Malara was partially supported by National Science Centre, Poland, Grant 2016/21/N/ST1/01491. The research of the Tomasz Szemberg and Justyna Szpond was partially supported by National Science Centre, Poland, Grant 2014/15/B/ST1/02197.
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Bauer, T., Malara, G., Szemberg, T. et al. Quartic unexpected curves and surfaces. manuscripta math. 161, 283–292 (2020). https://doi.org/10.1007/s00229-018-1091-3
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DOI: https://doi.org/10.1007/s00229-018-1091-3