Complex analytic variety

Imagine you have a big collection of shapes, like squares, circles, triangles, and so on. Now, let's say you take all of these shapes and put them together on a piece of paper. What you get is a big jumble of lines and curves that overlap and intersect each other.

This is kind of what a complex analytic variety is like. Instead of shapes, we have equations that describe curves and surfaces that are made up of complex numbers (numbers with a real and imaginary part). When we take all of these equations and put them together, we get a complicated object that has many different parts.

Like the jumble of shapes on a piece of paper, a complex analytic variety can be very messy and hard to understand. But just like we can pick out individual shapes in the jumble, we can study specific parts of the complex analytic variety by looking at its individual equations and how they interact with each other.

Some complex analytic varieties might look smooth and perfectly curved, like a ball or a doughnut. Others might look more crumpled and twisted, with sharp corners and edges. But no matter what they look like, they are all made up of a bunch of equations that fit together in some way.

So, in summary, a complex analytic variety is a complicated mathematical 'thing' that can be thought of as a bunch of overlapping equations that describe curves and surfaces made up of complex numbers. It can be very hard to understand, but by studying the individual equations and how they fit together, we can learn a lot about this fascinating object.