ADE Classification of Hypersurface Singularities over Local Rings

2025/09/18 by Yotam Svoray, Svoray, Yotam · 1 citation
Mathematics · #13C14 #13H10 #14B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2509.15396

openalex publication_date 2025/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present an ADE-type classification of hypersurfaces of complete regular local rings based on their Cohen-Macaulay type. In order to preform this classification, we show how we can generalize the classical result regarding finite and countable Cohen-Macaulay type to larger cardinalities, depending on the cardinality of the residue field.

Citations

• Singular loci of algebras over ramified discrete valuation rings
• On simple singularities and Weyl monodromy actions in mixed characteristic
• Infinite prime avoidance
• On finite determinacy for matrices of power series
• Finite determinacy of matrices over local rings.II. Tangent modules to\n the miniversal deformations for group-actions involving the ring\n automorphisms
• The Theory of Witt Vectors
• On two dimensional mixed characteristic rings of finite Cohen Macaulay type
• An uncountably infinite number of indecomposable totally reflexive modules
• On the structure and ideal theory of complete local rings

Cited by

• Detecting and Quantifying Isolated Singularities over Discrete Valuation Rings

Related

• Upper bounds for dimensions of singularity categories
• Maximal Cohen-Macaulay modules that are not locally free on the punctured spectrum
• Blowups of hypersurfaces
• Local Picard Groups
• On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type