Semistable reduction over thick log points

TL;DR

This paper extends semistable reduction theorems to log points with nilpotent structures, broadening classical desingularization methods to non-reduced schemes with principal nilradicals.

Contribution

It introduces a semistable reduction theorem over non-trivial nilpotent log points, expanding desingularization techniques to more general schemes.

Findings

Established semistable reduction over non-reduced log points.

Extended desingularization theories to schemes with nilpotent structures.

Provided new tools for handling singularities in algebraic geometry.

Abstract

We establish a version of a semistable reduction theorem over a log point with a non-trivial nilpotent structure. In order to do this we extend the classical desingularization theories to non-reduced schemes with generically principal nilradical.