Cartier Divisor

A Cartier divisor is a mathematical concept used in algebraic geometry to describe certain "divisors" on a geometric object, like a curve or surface. Think of it as a formal way to keep track of where a function vanishes or has poles—essentially, the points and the multiplicities (how many times it vanishes or poles) involved. Cartier divisors are represented locally by regular functions—nothing too complicated—making them a flexible and powerful tool for understanding the structure of algebraic shapes. They help mathematicians study how these shapes behave, intersect, and transform.