Cr\'onica de un contraejemplo

TL;DR

This paper narrates the history of Nash's method for resolving singularities, highlighting its initial promise and subsequent failure in general cases over five decades.

Contribution

It provides a historical and critical analysis of Nash's blowup method, illustrating its limitations and the evolution of understanding in singularity resolution.

Findings

Nash's method was initially promising for resolving singularities.

The method ultimately fails in general cases after five decades of research.

The paper offers a historical perspective on the development and limitations of Nash's approach.

Abstract

In the 1960s, John Nash proposed a method to resolve singularities. Five decades of encouraging results could not prevent an unexpected ending: the method does not work in general. In this note (written in Spanish), we tell the story of the rise and fall of the Nash blowup.