Comptes Rendus
Algebraic Geometry
Diminished Fermat-type arrangements and unexpected curves
Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 603-608.

The purpose of this note is to present and study a new series of the so-called unexpected curves. They enjoy a surprising property to the effect that their degree grows to infinity, whereas the multiplicity at a general fat point remains constant, equal 3, which is the least possible number appearing as the multiplicity of an unexpected curve at its singular point. We show that additionally the BMSS dual curves inherits the same pattern of behaviour.

Published online:
DOI: 10.5802/crmath.77
Classification: 14C20, 14N10, 14N20

Jakub Kabat 1; Beata Strycharz-Szemberg 2

1 Department of Mathematics, Pedagogical University of Cracow, Podchorazych 2, PL-30-084 Kraków, Poland
2 Department of Mathematics, Cracow University of Technology, Warszawska 24, PL-31-155 Kraków, Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Jakub Kabat and Beata Strycharz-Szemberg},
     title = {Diminished {Fermat-type} arrangements and unexpected curves},
     journal = {Comptes Rendus. Math\'ematique},
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Jakub Kabat; Beata Strycharz-Szemberg. Diminished Fermat-type arrangements and unexpected curves. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 603-608. doi : 10.5802/crmath.77.

[1] Thomas Bauer; Grzegorz Malara; Tomasz Szemberg; Justyna Szpond Quartic unexpected curves and surfaces, Manuscr. Math., Volume 161 (2020) no. 3-4, pp. 283-292 | DOI | MR | Zbl

[2] Luca Chiantini; Juan Migliore Sets of points which project to complete intersections (2019) | arXiv

[3] David Cook II; Brian Harbourne; Juan Migliore; Uwe Nagel Line arrangements and configurations of points with an unexpected geometric property, Compos. Math., Volume 154 (2018) no. 10, pp. 2150-2194 | DOI | MR | Zbl

[4] Roberta Di Gennaro; Giovanna Ilardi; Jean Vallès Singular hypersurfaces characterizing the Lefschetz properties, J. Lond. Math. Soc., Volume 89 (2014) no. 1, pp. 194-212 | DOI | MR | Zbl

[5] Marcin Dumnicki; Łucja Farnik; Brian Harbourne; Grzegorz Malara; Justyna Szpond; Halszka Tutaj-Gasińska A matrixwise approach to unexpected hypersurfaces, Linear Algebra Appl., Volume 592 (2020), pp. 113-133 | DOI | MR | Zbl

[6] Giuseppe Favacchio; Elena Guardo; Brian Harbourne; Juan Migliore Expecting the unexpected: quantifying the persistence of unexpected hypersurfaces (2020) | arXiv

[7] Brian Harbourne; Juan Migliore; Uwe Nagel; Zach Teitler Unexpected hypersurfaces and where to find them (2018) (to appear in Mich. Math. J.) | arXiv

[8] Brian Harbourne; Juan Migliore; Halszka Tutaj-Gasińska New constructions of unexpected hypersurfaces in N (2019) | arXiv

[9] Justyna Szpond Fermat-type arrangements (2019) | arXiv

[10] Justyna Szpond Unexpected hypersurfaces with multiple fat points (2019) | arXiv

[11] Justyna Szpond Unexpected curves and Togliatti–type surfaces, Math. Nachr., Volume 293 (2020), pp. 158-168 | DOI | Zbl

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