Related papers: Log canonical thresholds in positive characteristi…

In this paper we study singularities in arbitrary characteristic. We propose Finite Determination Conjecture for Mather-Jacobian minimal log discrepancies in terms of jet schemes of a singularity. The conjecture is equivalent to the…

In this paper, we initiate our investigation of log canonical models for the moduli space of curves with the boundary divisor $\a \d$ as we decrease $\a$ from 1 to 0. We prove that for the first critical value $\a = 9/11$, the log canonical…

We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…

In this paper, we introduce the notion of a characteristic-zero lifting of an object in positive characteristic by means of ``skeletons''. Using this notion, we relate invariants of singularities in positive characteristic to their…

We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric…

Motivated by Shokurov's ACC Conjecture for log canonical thresholds, we propose an inductive point of view on singularities of pairs, in the case when the ambient variety is smooth. Our main result characterizes the log canonicity of a pair…

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the…

Let $f:X\to U$ be a projective morphism of normal varieties and $(X,\Delta)$ a dlt pair. We prove that if there is an open set $U^0\subset U$, such that $(X,\Delta)\times_U U^0$ has a good minimal model over $U^0$ and the images of all the…

We prove dimension bounds on the jet schemes of the variety of nilpotent matrices (and of related varieties) in positive characteristic. This result has applications to the analytic properties of the Chevalley map that sends a matrix to its…

In this paper, we prove a `cut-by-curves criterion' for an overconvergent isocrystal on a smooth variety over a field of characteristic $p>0$ to extend logarithmically to its smooth compactification whose complement is a strict normal…

In this paper we characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of…

We show that a weak version of the canonical bundle formula holds for fibrations of relative dimension one. We provide various applications thereof, for instance, using the recent result of Xu and Zhang, we prove the log non-vanishing…

We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the…

In this article we prove the following boundedness result: Fix a DCC set $I\subset [0, 1]$. Let $\mathfrak{D}$ be the set of all log pairs $(X, \Delta)$ satisfying the following properties: (i) $X$ is a projective surface defined over an…

In this short note, we consider the conjecture that the log canonical divisor (resp. the anti-log canonical divisor) $K_X + \Delta$ (resp. $-(K_X + \Delta)$) on a pair $(X, \Delta)$ consisting of a complex projective manifold $X$ and a…

Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter…

In characteristic zero, quotient singularities are log terminal. Moreover, we can check whether a quotient variety is canonical or not by using only the age of each element of the relevant finite group if the group does not have…

We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a…

In this paper we give a complete description of the irreducible components of the jet schemes (with origin in the singular locus) of a two-dimensional quasi-ordinary hypersurface singularity. We associate with these components and with…

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…