Hypersurfaces with many Aj-singularities: explicit constructions

A construction of algebraic surfaces based on two types of simple arrangements of lines, containing the prototiles of substitution tilings, has been proposed recently. The surfaces are derived with the help of polynomials obtained from products of the lines generating the simple arrangements. One of the arrangements gives the generalizations of the Chebyshev polynomials known as folding polynomials. The other produces a family of polynomials having more critical points with the same critical values, which can also be used to derive hypersurfaces with many Aj-singularities.