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arXiv · 1808.07321

Nondiscreteness of $F$-thresholds

Vijaylaxmi Trivedi
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Abstract

We give examples of two dimensional normal ${\mathbb Q}$-Gorenstein graded domains, where the set of $F$-thresholds of the maximal ideal is not discrete, thus answering a question by Musta\c{t}\u{a}-Takagi-Watanabe. We also prove that, for a two dimensional standard graded domain $(R, {\bf m})$ over a field of characteristic $0$, with graded ideal $I$, if $({\bf m}_p, I_p)$ is a reduction mod $p$ of $({\bf m}, I)$ then $c^{I_p}({\bf m}_p) \neq c^I_{\infty}({\bf m})$ implies $c^{I_p}({\bf m}_p)$ has $p$ in the denominator.

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Vijaylaxmi Trivedi. 2018-08-22. Nondiscreteness of $F$-thresholds. https://arxiv.org/abs/1808.07321

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