GIT Quotients

GIT quotients are a mathematical tool used in algebraic geometry to construct new, simpler spaces from complex ones with symmetries. Imagine a shape with a group of transformations (like rotations or reflections) that leave some properties unchanged. GIT quotienting essentially "divides out" these symmetries, producing a space that represents the original shape without redundant or symmetrical parts. This process helps mathematicians study complicated geometric objects by distilling their essential structure, enabling a better understanding of their properties and relationships in a more manageable form.