Divisor (algebraic geometry)
Okay, let's say there are some numbers (like 4, 8, 12, 16 and so on) that you can divide by 2 and get a whole number. We call 2 a "divisor" of those numbers - it's a number that can divide those numbers evenly.
In algebraic geometry, we're looking at shapes called "varieties." But instead of numbers, we have "functions" that describe these shapes. And just like with numbers, we can talk about divisors of those functions.
A divisor is just a way of counting how many roots a function has at different points on the shape. Imagine you have a plant - you can count how many roots it has by looking at the points where the roots come out of the ground. In algebraic geometry, we do something similar but with functions on shapes instead of plants.
So a divisor might say something like "this function has 2 roots at this point and 1 root at this other point, but no roots anywhere else on the shape." We use divisors to help us understand the properties of the shapes we're looking at and how the functions behave on those shapes.
In algebraic geometry, we're looking at shapes called "varieties." But instead of numbers, we have "functions" that describe these shapes. And just like with numbers, we can talk about divisors of those functions.
A divisor is just a way of counting how many roots a function has at different points on the shape. Imagine you have a plant - you can count how many roots it has by looking at the points where the roots come out of the ground. In algebraic geometry, we do something similar but with functions on shapes instead of plants.
So a divisor might say something like "this function has 2 roots at this point and 1 root at this other point, but no roots anywhere else on the shape." We use divisors to help us understand the properties of the shapes we're looking at and how the functions behave on those shapes.