Related papers: Local m-adic constancy of F-pure thresholds and te…

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…

Using the Frobenius map, we introduce a new invariant for a pair $(R,\a)$ of a ring $R$ and an ideal $\a \subset R$, which we call the F-pure threshold $\mathrm{c}(\a)$ of $\a$, and study its properties. We see that the F-pure threshold…

Blickle, Musta\c{t}\u{a} and Smith proposed two conjectures on the limits of $F$-pure thresholds. One conjecture asks whether or not the limit of a sequence of $F$-pure thresholds of principal ideals on regular local rings of fixed…

In this paper, we prove that the set of all $F$-pure thresholds of ideals with fixed embedding dimension satisfies the ascending chain condition. As a corollary, given an integer $d$, we verify the ascending chain condition for the set of…

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…

We prove that if $f$ is a reduced homogenous polynomial of degree $d$, then its $F$-pure threshold at the unique homogeneous maximal ideal is at least $\frac{1}{d-1}$. We show, furthermore, that its $F$-pure threshold equals $\frac{1}{d-1}$…

The $F$-pure threshold is a numerical invariant of prime characteristic singularities, that constitutes an analogue of the log canonical thresholds in characteristic zero. We compute the $F$-pure thresholds of determinantal ideals, i.e., of…

We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a…

We continue our study of F-thresholds begun in math/0607660 by an in depth analysis of the hypersurface case. We use the D--module theoretic description of generalized test ideals which allows us to show that in any F--finite regular ring…

It is well known that nice conditions on the canonical module of a local ring have a strong impact in the study of strong F-regularity and F-purity. In this note, we prove that if (R,m) is an equidimensional and S_2 local ring that admits a…

We compute the $F$-pure threshold of some non-principal ideals which satisfy a geometric generic condition about their Newton polyhedron. We also contribute some evidence in favor of the conjectured equality between the $F$-pure threshold…

We give a value for the $F$-pure threshold at the maximal homogeneous ideal $\mathfrak{m}$ of the symmetric determinantal ring over a field of prime characteristic. The answer is characteristic independent, so we immediately get the log…

Let $(R, \mathfrak{m})$ be a regular local ring of characteristic $p > 0$. Among all proper ideals $\mathfrak{a}\subseteq R$ with a fixed order of vanishing $\text{ord}_{\mathfrak{m}}(\mathfrak{a})$, we classify the ideals for which the…

F-thresholds are defined by Mustata, Takagi and Watanabe in [F-thresholds and Bernstein-Sato polynomials], which are invariants of the pair of ideals on rings of characteristic $p$. In their paper, it is proved F-thresholds equal to jumping…

Introduced by Takagi and Watanabe, the F-pure threshold is an invariant defined in terms of the Frobenius homomorphism. While it finds applications in various settings, it is primarily used as a local invariant. The purpose of this note is…

In this note, we use estimates given in the recent preprint [Her11b]to deduce a formula for the F-pure threshold of a binomial hypersurface over a field of prime characteristic. These formulas are given in terms of the associated splitting…

This paper studies the jumping coefficients of principal ideals of regular local rings. Recently M. Blickle, M. Mustata and K. Smith showed that, when $R$ is of essentially finite type over a field and $F$-finite, bounded intervals contain…

In this note, we derive a formula for the F-pure threshold of diagonal hypersurfaces over a perfect field of prime characteristic. We also calculate the associated test ideal at the F-pure threshold, and give formulas for higher jumping…

We provide a formula for $F$-thresholds of a Thom-Sebastiani type polynomial over a perfect field of prime characteristic. This result extends the formula for the $F$-pure threshold of a diagonal hypersurface. We also compute the first test…

In this article, we study certain local cohomology modules over $F$-pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for computing these invariants when the $F$-pure ring is standard…