Quotient Varieties

A quotient variety is a mathematical construction that describes how a larger space can be simplified by grouping points that are related through symmetries or transformations. Imagine you have a shape with symmetry—like a square, where rotating it by 90 degrees doesn't change its appearance. The quotient variety captures this idea by "dividing out" these symmetries, creating a new space that represents the original shape but considers points related by the symmetry as one. This process helps mathematicians analyze complex structures by focusing on their essential features without redundancy.