Related papers: The set of toric minimal log discrepancies
We survey the known and expected properties of the minimal log discrepancy, the local invariant of a log variety.
We compute the Mather minimal log discrepancy via jet schemes and arc spaces for toric varieties and very general hypersurfaces.
This is the major revision. The main purpose of this paper is to prove that minimal discrepancies of $n$-dimensional toric singularities can accumulate only from above and only to minimal discrepancies of toric singularities of dimension…
An explanation to the boundness of minimal log discrepancies conjectured by V.V. Shokurov would be that the minimal log discrepancies of a variety in its closed points define a lower semi-continuous function. We check this lower…
The minimal log discrepancy is an invariant of singularities that plays an important role in the birational classification of algebraic varieties. Shokurov conjectured that the minimal log discrepancy can always be bounded from above in…
The second largest accumulation point of the set of minimal log discrepancies of threefolds is $\frac{5}{6}$. In particular, the minimal log discrepancies of $\frac{5}{6}$-lc threefolds satisfy the ACC.
We show the semi-continuity property of minimal log discrepancies for varieties which have a crepant resolution in the category of Deligne-Mumford stacks. Using this property, we also prove the ideal-adic semi-continuity problem for toric…
We classify two-dimensional toric log germs in terms of their minimal log discrepancy.
This paper formulates the Nash problem for a pair consisting of a toric variety and an invariant ideal and gives an affirmative answer to the problem. We also prove that the minimal log-discrepacy is computed by a divisor corresponding to a…
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…
We generalize the rationality theorem of the accumulation points of log canonical thresholds which was proved by Hacon, M\textsuperscript{c}Kernan, and Xu. Further, we apply the rationality to the ACC problem on the minimal log…
We formulate a comparison of minimal log discrepancies of a variety and its ambient space with appropriate boundaries in terms of motivic integration. It was obtained also by Ein and Musta\c{t}\v{a} independently.
For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.
We prove the ACC for minimal log discrepancies on an arbitrary fixed threefold.
We prove the ideal-adic semi-continuity of minimal log discrepancies on surfaces.
We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs $\bigl(D^k,\sum \alpha_i D^{k_i}\bigr)$ consisting of a determinantal variety (of square matrices) and an $\mathbb R$-linear…
We study a divisor computing the minimal log discrepancy on a smooth surface. Such a divisor is obtained by a weighted blow-up. There exists an example of a pair such that any divisor computing the minimal log discrepancy computes no log…
We study the distribution of integral points on log varieties.
We translate the equivariant decomposition theorem (in the case of a proper morphism of toric varieties) in to the language of combinatorially defined ``shifted minimal complexes''.
In this article, we use the cone of nef curves to study minimal log discrepancies. The first result is an improvement of the nef cone theorem in the case of log Calabi-Yau dlt pairs. Then, we prove that the ascending chain condition for…