☰ George D. Torres

About this image

Shown here is the perturbation of a singular complex variety. Take the product p of three linear polynomials with complex coefficients, so that the corresponding variety V(p) is the union of three complex lines (Riemann spheres). Then perturbing p by a small homogenous monomial will produce the smooth variety shown here. Topologically this operation replaces the singular points with cylinders in a connect sum to produce a genus 1 complex surface.