The Nash Map

The Nash Map is a concept in mathematics that helps understand how different geometric spaces, called "varieties," relate to each other through their singularities (points where they aren’t smooth). It connects the space of all possible ways to "resolve" these singularities (called the "resolution space") with the original space containing the singular points. The Nash Map is a specific function that matches each special feature in the resolution to a corresponding singularity in the original space. It aims to uncover how these singularities can be systematically smoothed or understood via their resolutions, providing insights into the structure of algebraic varieties.