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The purpose of this note is to revisit the results of arXiv:1407.4324 from a slightly different perspective, outlining how, if the integral closures of a finite set of prime ideals abide the expected convexity patterns, then the existence of a peculiar polynomial allows to compute the F-jumping numbers of all the ideals formed by taking sums of products of the original ones. The note concludes with the suggestion of a possible source of examples falling in such a framework.
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 Mustac{t}u{a}-Takagi-Watanabe. We also prove that, for a two dimen
The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite fields relati
We had shown earlier that for a standard graded ring $R$ and a graded ideal $I$ in characteristic $p>0$, with $ell(R/I) <infty$, there exists a compactly supported continuous function $f_{R, I}$ whose Riemann integral is the HK multiplicity $e_{HK}(R
In this article, we investigate F-pure thresholds of polynomials that are homogeneous under some N-grading, and have an isolated singularity at the origin. We characterize these invariants in terms of the base p expansion of the corresponding log can
Let $(A,mathfrak{m})$ be an analytically unramified formally equidimensional Noetherian local ring with $ depth A geq 2$. Let $I$ be an $mathfrak{m}$-primary ideal and set $I^*$ to be the integral closure of $I$. Set $G^*(I) = bigoplus_{ngeq 0} (I^n