Idealistic Flowers in the Reduction of Singularities

TL;DR

This paper introduces the concept of 'idealistic flowers' to provide a proof of the classical reduction of singularities, leveraging maximal contact theory to address globalization issues in singularity resolution.

Contribution

It offers a novel proof framework for singularity reduction using idealistic flowers, building on recent developments in maximal contact theory.

Findings

Proof of classical reduction of singularities established

Addresses globalization issues in maximal contact theory

Builds on recent advances in algebraic geometry

Abstract

We present here a proof of the classical reduction of singularities based on the idea of "idealistic flowers". We follow the general ideas of Maximal Contact Theory, presented in a recent book of Aroca, Hironaka and Vicente, that recovers three old publications of Jorge Juan Institute. The concept of idealistic flowers deals with the globalization problems arising from the local nature of the maximal contact.