Fulton–MacPherson intersection theory

Fulton–MacPherson intersection theory is a mathematical framework that rigorously studies how geometric objects, like shapes or spaces, intersect or overlap. It develops tools to analyze intersections even when objects meet in complicated ways—such as overlapping with multiplicities or singularities—by "resolving" these complexities into a structured, algebraic setting. This theory extends traditional intersection concepts, enabling precise calculations and classifications in advanced geometry, algebra, and topology, and has applications in areas like enumerative geometry and string theory. Essentially, it provides a systematic way to understand and quantify how geometric entities intersect within complex spaces.