Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

Abstract

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

26 pages; minor changes have been added

References in corpus (5)

• Canonical embedded and non-embedded resolution of singularities for excellent two-dimensional schemes
• Singularities in positive characteristic, stratification and simplification of the singular locus
• Rees algebras and resolution of singularities
• Rees algebras on smooth schemes: integral closure and higher differential operators
• Kangaroo points and oblique polynomials in resolution of positive characteristic

Cited by in corpus (13)

• Resolution of Singularities of Arithmetical Threefolds II
• Blowups and Resolution
• Nash multiplicity sequences and Hironaka's order function
• Resolution of singularities of an idealistic filtration in dimension 3 after Benito-Villamayor
• On Rees algebras and invariants for singularities over perfect fields
• Finite Generation of Extensions of Associated Graded Rings Along a Valuation
• Embedded desingularization for arithmetic surfaces -- toward a parallel implementation
• A New Proof for the Embedded Resolution of Surface Singularities in Arbitrary Characteristic
• A new strategy for resolution of singularities in the monomial case in positive characteristic
• On the simplification of singularities by blowing up at equimultiple centers
• Finite morphisms and Nash multiplicity sequences
• The asymptotic Samuel function and invariants of singularities
• Contact loci and Hironaka's order