On plane conic arrangements with $$A_{5}$$ and $$A_{7}$$ singularities

Abstract

AbstractIn the present note we provide combinatorial constraints on certain conic arrangements in the plane admitting $$A_{5}$$ A 5 and $$A_{7}$$ A 7 singularities. As a corollary, we provide upper bounds on the number of $$A_{5}$$ A 5 and $$A_{7}$$ A 7 singularities for such arrangements.