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arXiv · 1502.07236

On tautness of two-dimensional $F$-regular and $F$-pure rational singularities

Yuki Tanaka
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Abstract

The weighted dual graph of a two-dimensional normal singularity $(X, x)$ represents the topological nature of the exceptional locus of its minimal log resolution. $(X, x)$ and its graph are said to be taut if the singularity can be uniquely determined by the graph. Laufer gave a complete list of taut singularities over $\mathbb{C}$. In positive characteristics, taut graphs over $\mathbb{C}$ are not necessarily taut and tautness have been studied only for special cases. In this paper, we prove the tautness of $F$-regular singularities. We also discuss the tautness of $F$-pure rational singularities.

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Yuki Tanaka. 2015-02-25. On tautness of two-dimensional $F$-regular and $F$-pure rational singularities. https://arxiv.org/abs/1502.07236

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