A complex torus is a mathematical structure that arises in the field of complex geometry. It can be visualized as a higher-dimensional version of a doughnut shape, where the surface is defined using complex numbers. Specifically, a complex torus is formed by taking a complex vector space and identifying points that differ by lattice points, creating a periodic structure. In more technical terms, a complex torus can be represented as the quotient of a complex vector space by a discrete subgroup of translations, known as a lattice. This concept is closely related to elliptic curves and has applications in various areas of mathematics, including algebraic geometry and number theory.