Finite morphism

Imagine you have a big piece of paper and a smaller piece of paper. When you place the smaller piece of paper on the big one, it completely covers a part of the big paper. This is what it means for the smaller paper to be finite on the bigger paper.

Similarly, in math, when we talk about a finite morphism, we are talking about two mathematical objects, called algebraic varieties, which are like shapes in mathematics.

Let's say we have two algebraic varieties, let's call them X and Y. Now, when we say that there is a finite morphism from X to Y, it means that we can imagine X sitting on top of Y, just like the smaller paper on the bigger paper, and it completely covers a part of Y. But instead of paper, we are talking about shapes in math.

In this case, the finite morphism from X to Y will preserve certain properties. It will preserve the number of points on each shape, which is like a dot on the shape that we can imagine. It will also preserve other mathematical structures, like lines or curves, that exist in X and Y.

So, to summarize, a finite morphism is a mathematical relationship between two shapes, where one shape completely covers a part of the other shape, while preserving the number of points and other mathematical structures.