Quotient scheme

A Quotient scheme is a mathematical construction used in algebraic geometry to simplify complex geometric objects called "schemes." It involves partitioning a scheme into equivalence classes (or identifying points that behave similarly) and then creating a new, “quotient” scheme that captures these classes as single points. This process allows mathematicians to study the structure of the original scheme by focusing on these broader groupings, helping to understand how objects relate or evolve under certain transformations. Essentially, a Quotient scheme provides a systematic way to reduce complexity and analyze the shape and structure of geometric entities.