On Rees algebras and invariants for singularities over perfect fields

TL;DR

This paper explores the application of Rees algebras to analyze singularities in smooth schemes over perfect fields, especially when hypersurface multiplicities relate to the field's characteristic, simplifying resolution issues.

Contribution

It demonstrates new applications of Rees algebras in studying singularities and addresses local-global questions in resolution of singularities over characteristic zero fields.

Findings

Rees algebras effectively analyze singularities over perfect fields.

The approach simplifies local-global resolution questions.

Applications to hypersurfaces with multiplicities related to characteristic.

Abstract

The purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations in which the multiplicity of a hypersurface is a multiple of the characteristic. As another application, here we indicate how the use of these algebras has trivialized local-global questions in resolution of singularities over fields of characteristic zero.