Serre's criterion

Serre's criterion is a test used to determine whether a specific type of mathematical structure, known as a variety, has certain desirable properties, specifically smoothness or regularity. It states that if a variety can be represented in a certain way using simpler components, and if those components meet certain conditions, then the entire variety will also meet those conditions. This criterion helps mathematicians understand complex shapes and spaces in algebraic geometry, making it easier to analyze and classify them based on their geometric and algebraic features.