Some lower bounds for the maximal number of A -singularities in algebraic surfaces

Key Points

• The research aims to establish lower bounds for the maximal number of A-singularities in algebraic surfaces.
• Constructed algebraic surfaces using bivariate polynomials
• Utilized previous works on nodal surfaces and Belyi polynomials
• Derived explicit expressions involving classical Jacobi polynomials
• Demonstrated the construction of surfaces with a significantly high number of A-singularities
• Provided new explicit expressions for certain polynomial families