Nondiscreteness of $F$-thresholds

• DOI: 10.4310/mrl.2020.v27.n6.a13
• Publication Date: 2021-02-17T22:47:16Z
• Authors: Vijaylaxmi Trivedi
• Keywords: Mathematics - Algebraic Geometry; 13A35, 13A02, 14H60; FOS: Mathematics; 0101 mathematics; Mathematics - Commutative Algebra; Commutative Algebra (math.AC); Algebraic Geometry (math.AG); 01 natural sciences

9 pages<br/>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����-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.<br/>