Divisor class group

The divisor class group is a mathematical concept used in algebraic geometry and number theory to study the properties of algebraic curves and their divisors. It classifies divisors (formal sums of points on a curve) up to a certain equivalence called linear equivalence, which considers divisors differing by a principal divisor (divisor of a rational function). Essentially, it groups divisors into classes that share similar geometric or arithmetic properties, providing insight into the structure of the curve. The divisor class group helps mathematicians understand functions, mappings, and rational points on algebraic varieties.