Elimination with applications to singularities in positive characteristic

TL;DR

This paper explores the use of elimination theory to address singularities and resolution problems in algebraic geometry over fields of positive characteristic, extending concepts from characteristic zero.

Contribution

It introduces a partial extension of resolution functions from characteristic zero to positive characteristic using elimination theory.

Findings

Partial resolution function extension achieved

Applicable to singularity analysis in positive characteristic

Advances understanding of resolution in algebraic geometry

Abstract

We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of characteristic zero, is discussed here in positive characteristic.