Singularities in Positive Characteristic

TL;DR

This survey explores the nature of singularities in algebraic varieties over fields of positive characteristic, highlighting differences from zero characteristic and discussing classification, equisingularity, and open problems.

Contribution

It provides a comprehensive overview of singularities in positive characteristic, emphasizing differences from zero characteristic and summarizing key results and open questions.

Findings

Differences between positive and zero characteristic singularities

Classification of hypersurface singularities

Open problems in equisingularity theory

Abstract

In this survey paper we give an overview on some aspects of singularities of algebraic varieties over an algebraically closed field of arbitrary characteristic. We review in particular results on equisingularity of plane curve singularities, classification of hypersurface singularities and determinacy of arbitrary singularities. The section on equisingularity has its roots in two important early papers by Antonio Campillo. One emphasis is on the differences between positive and zero characteristic and on open problems.