Projective variety

Imagine you have a magical box that can take any shape you want it to. You can stretch it, twist it, and turn it around however you like. This box is like a projective variety!

A projective variety is a special kind of shape that can be manipulated using something called projective space. This space is like the big room the magical box is in, and it has special rules that govern how the box can move around without changing its shape.

In order to define a projective variety, we have to start with a collection of equations that describe its shape. These equations tell us things like where the edges are, how curvy the shape is, and how it looks from different angles.

Once we have these equations, we can use projective space to study the shape further. This involves thinking about how the shape looks when we look at it from different perspectives, and how it changes as we move it around.

Projective varieties are important because they help us understand some of the most fundamental structures in mathematics. They are used in everything from geometry and algebra to physics and computer science. By studying projective varieties, we can unlock the mysteries of the universe and gain new insights into the world around us!