no. 5
Géométrie algébrique
Diminished Fermat-type arrangements and unexpected curves
Kabat, Jakub1 ; Strycharz-Szemberg, Beata2
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, Tome 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.

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DOI : 10.5802/crmath.77
Classification : 14C20, 14N10, 14N20
Kabat, Jakub 1 ; Strycharz-Szemberg, Beata 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 
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Kabat, Jakub; Strycharz-Szemberg, Beata. Diminished Fermat-type arrangements and unexpected curves. Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 603-608. doi : 10.5802/crmath.77. http://www.numdam.org/articles/10.5802/crmath.77/

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