algebraic cycle

An algebraic cycle is a formal combination of geometric shapes called subvarieties within a larger space, such as a shape or space defined by polynomial equations. Think of it like a weighted collection of different layers or pieces (like lines, surfaces, or points) inside a bigger object, where each piece is associated with a multiplicity or coefficient. These cycles help mathematicians study how these shapes interact, intersect, and relate within the space, serving as fundamental objects in algebraic geometry for understanding the structure and properties of complex geometric entities.