Diminished Fermat-type arrangements and unexpected curves

Abstract

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.