Comptes Rendus
no. 5
Algebraic Geometry
Diminished Fermat-type arrangements and unexpected curves
Jakub Kabat1; Beata Strycharz-Szemberg2
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
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.

Received:
Revised:
Accepted:
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 
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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.77/

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