Abstract
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 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 which generates surfaces having more real nodes, and they can also be used, in combination with Belyi polynomials, to derive hypersurfaces in the complex projective space with many Aj-singularities. In some cases explicit expressions can be obtained from the classical Jacobi polynomials. The lower bounds for the maximum possible number of Aj-singularities in certain hypersurfaces of degree d are improved for several values of d and j.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
