complex tori

A complex torus is a mathematical shape formed by taking a two-dimensional complex plane (which can be thought of as a fancy version of the ordinary plane) and wrapping it around itself using a specific pattern of repeated shifts called a lattice. Imagine a sheet of paper folded and identified so that opposite edges match, creating a surface with a doughnut-like shape called a torus. When using complex numbers, this construction results in a complex torus—a shape that combines the properties of the complex plane with the topology of a torus—important in areas like algebraic geometry and complex analysis.