Classification of two-dimensional F-regular and F-pure singularities
The notions of \(F\)-regularity and \(F\)-purity for rings of characteristic \(p>0\) were introduced by \textit{M. Hochster} and \textit{C. Huneke} [J. Am. Math. Soc. 3, No. 1, 31-116 (1990; Zbl 0701.13002)]and \textit{M. Hochster} and \textit{J. L. Roberts} [Adv. Math. 21, 117-172 (1976; Zbl 0348.13007)], respectively. Later \textit{V. B. Mehta} and \textit{V. Srinivas} [J. Algebra 143, No. 1, 130-143 (1991; Zbl 0760.14012)] studied two-dimensional normal \(F\)-pure singularities and proved that such a singularity is either (a) a simple elliptic singularity with an ordinary elliptic exceptional curve, (b) a cusp singularity, or (c) a rational singularity and that a singularity of the first two types is \(F\)-pure. However, being a rational singularity is not sufficient to be \(F\)-pure. -- This papers continues the study of two-dimensional \(F\)-regular and rational \(F\)-pure singularities and completes the classification of these singularities in terms of the dual graph of the minimal resolution and the characteristic \(p\).
scientific article; zbMATH DE number 1123530
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