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Comptes Rendus. Mathématique
Géométrie algébrique
Diminished Fermat-type arrangements and unexpected curves
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.

Reçu le : 2020-03-10
Révisé le : 2020-04-15
Accepté le : 2020-05-22
Publié le : 2020-09-14
DOI : https://doi.org/10.5802/crmath.77
Classification : 14C20,  14N10,  14N20
     author = {Jakub Kabat and Beata Strycharz-Szemberg},
     title = {Diminished Fermat-type arrangements and unexpected curves},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {603--608},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.77},
     language = {en},
     url = {comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_5_603_0/}
Jakub Kabat; Beata Strycharz-Szemberg. Diminished Fermat-type arrangements and unexpected curves. Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 603-608. doi : 10.5802/crmath.77. https://comptes-rendus.academie-sciences.fr/mathematique/item/CRMATH_2020__358_5_603_0/

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