Algebraic cycles

Algebraic cycles are mathematical objects used in algebraic geometry, a field that studies geometric shapes defined by polynomial equations. They essentially represent collections of points, lines, surfaces, or higher-dimensional shapes in a way that captures their geometric and algebraic properties. Algebraic cycles can be used to analyze complex structures, like the relationships between different shapes, and play a crucial role in understanding the topology and invariants of these shapes. They help mathematicians explore deep connections within mathematics, influencing areas such as number theory and mathematical models.