Deformations of isolated cyclic quotient singularities in arbitrary characteristic

2025/11/28 by Pfeifer, Matthias
Mathematics · #13A50 #14B07 #14J17 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.23382

openalex publication_date 2025/11/28 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We show that toric surface singularities deform to toric surface singularities - both in equal and mixed characteristic. As an application, we establish Riemenschneiders conjecture that isolated cyclic quotient singularities of any dimension deform to isolated cyclic quotient singularities in equal and mixed characteristic.

Citations

• Arithmetic and geometric deformations of F-pure and F-regular singularities
• Deformationen von Quotientensingularit�ten (nach zyklischen Gruppen)

Related

• P-Resolutions of Cyclic Quotients from the Toric Viewpoint
• Ordinary r--tuples in cyclic quotient surface singularities
• Linearly Reductive Quotient Singularities
• A homology plane of general type can have at most a cyclic quotient singularity
• Singularity content