Desingularisation
Desingularisation is a process in algebraic geometry and related fields that aims to resolve singularities of a geometric object, typically an algebraic variety or a scheme. Singularities are points where the object is not "smooth" in a geometric sense, meaning it might have sharp points, self-intersections, or other irregularities. These singularities can make it difficult to study the object's properties using standard calculus-based methods.
The goal of desingularisation is to replace the singular object with a smooth one, or at least
A key result in this area is Hironaka's theorem, which states that any algebraic variety over a
Desingularisation is a fundamental tool for understanding the geometry of singular varieties. It allows mathematicians to