On a family of complex algebraic surfaces of degree 3n

TL;DR

This paper investigates a specific class of complex algebraic surfaces of degree 3n with only ordinary double points, constructed via bivariate polynomials linked to affine Weyl groups, expanding understanding of their geometric properties.

Contribution

Introduces a new family of algebraic surfaces of degree 3n with controlled singularities, constructed using polynomials related to affine Weyl groups of type A2.

Findings

Construction of surfaces with only ordinary double points

Connection between algebraic surfaces and affine Weyl groups

Potential applications in algebraic geometry and singularity theory

Abstract

We study a class of algebraic surfaces of degree 3n in the complex projective space with only ordinary double points. They are obtained by using bivariate polynomials with complex coefficients related to the generalized cosine associated to the affine Weyl group of the root system A2.