Covers of rational double points in mixed characteristic
| Autor: | Karl Schwede, Linquan Ma, Thomas Polstra, Kevin Tucker, Javier Carvajal-Rojas |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Commutative Algebra
Rational surface Applied Mathematics Dimension (graph theory) isolated singularities Rational singularity Regular local ring surfaces Commutative Algebra (math.AC) Mathematics - Commutative Algebra Combinatorics Mathematics - Algebraic Geometry Regular scheme Cover (topology) FOS: Mathematics Maximal ideal Gravitational singularity Geometry and Topology rings Algebraic Geometry (math.AG) adjunction Mathematics |
| Zdroj: | Journal of Singularities. 23 |
| ISSN: | 1949-2006 |
| DOI: | 10.5427/jsing.2021.23h |
| Popis: | We further the classification of rational surface singularities. Suppose $(S, \mathfrak{n}, \mathcal{k})$ is a strictly Henselian regular local ring of mixed characteristic $(0, p > 5)$. We classify functions $f$ for which $S/(f)$ has an isolated rational singularity at the maximal ideal $\mathfrak{n}$. The classification of such functions are used to show that if $(R, \mathfrak{m}, \mathcal{k})$ is an excellent, strictly Henselian, Gorenstein rational singularity of dimension $2$ and mixed characteristic $(0, p > 5)$, then there exists a split finite cover of $\mbox{Spec}(R)$ by a regular scheme. We give an application of our result to the study of $2$-dimensional BCM-regular singularities in mixed characteristic. Comments welcome! |
| Databáze: | OpenAIRE |
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