Related papers: F-thresholds of hypersurfaces

We prove that if Y is a hypersurface of degree d in P^n with isolated singularities, then the log canonical threshold of (P^n,Y) is at least min{n/d,1}. Moreover, if d is at least n+1, then we have equality if and only if Y is the…

In this article we establish bounds for the Castelnuovo-Mumford regularity of projective schemes in terms of the degrees of their defining equations. The main new ingredient in our proof is to show that generic residual intersections of…

Let $\mathbb{F}_q$ be a finite field with $q=p^n$ elements. In this paper, we study the number of $\mathbb{F}_q$-rational points on the affine hypersurface $\mathcal X$ given by $a_1 x_1^{d_1}+\dots+a_s x_s^{d_s}=b$, where…

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…

We consider a quasi-homogeneous polynomial $f \in \mathbb{Z}[x_0, \ldots, x_N]$ of degree $w$ equal to the degree of $x_0 \cdots x_N$ and show that the $F$-pure threshold of the reduction $f_p \in \mathbb{F}_p[x_0, \ldots, x_N]$ is equal to…

The acquisition of the defining equations of Rees algebras is a natural way to study these algebras and allows certain invariants and properties to be deduced. In this paper, we consider Rees algebras of codimension 2 perfect ideals of…

Using the Tannakian formalism, we formulate conjectural analogs of Chebotar\"ev's Density Theorem for $F$-isocrystals over a smooth geometrically irreducible variety defined over a finite field. We prove these analogs for several large…

Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this behavior under flat maps with reasonably nice (but far from…

In this article we study F-pure thresholds (and, more generally, F-thresholds) of homogeneous polynomials in two variables over a field of characteristic p>0. Passing to a field extension, we factor such a polynomial into a product of…

We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the…

Sufficient conditions for an ideal $\mathcal I$ in $R\Mod$ to be covering are proved. This allows to obtain an alternative proof of the existence of phantom covers of modules. Our approach is inspired by an extension of the standard…

The notion of $p_g$-ideals for normal surface singularities has been proved to be very useful. On the other hand, the core of ideals has been proved to be very important concept and also very mysterious one. However, the computation of the…

A minimum depth d^I(S --> R) is assigned to a ring homomorphism S --> R and a R-R-bimodule I. The recent notion of depth of a subring d(S,R)in a paper by Boltje-Danz-Kuelshammer is recovered when I = R and S --> R is the inclusion mapping.…

We introduce higher $F$-rationality generalising $F$-rationality. We prove that a normal variety over a field of characteristic zero is $m$-rational if and only if it is $m$-$F$-rational after reduction modulo a sufficiently large prime…

We study the structure of $D$-modules over a ring $R$ which is a direct summand of a polynomial or a power series ring $S$ with coefficients over a field. We relate properties of $D$-modules over $R$ to $D$-modules over $S$. We show that…

Let X be a smooth variety over a field of characteristic p>0. We prove that the forgetful functor from the category of overconvergent F-isocrystals on X to the category of convergent F-isocrystals is fully faithful. The argument uses the…

We consider the question of determining the maximum number of $\mathbb{F}_q$-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field $\mathbb{F}_q$, or in other words, the…

Let \(X\subset \mathbb{P}^{n+1}\) be a smooth cubic hypersurface, and let \(F(X)\) be the variety of lines on \(X\). We prove the surjectivity of the cylinder maps on the Chow groups of \(F(X)\) and \(X\) if \(X\) contains a one-cycle of…

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…

The set of all maximal ideals of the ring $\mathcal{M}(X,\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\hat{X}$ of…