On minimal log discrepancies

@article{Ambro1999OnML,
  title={On minimal log discrepancies},
  author={Florin Ambro},
  journal={Mathematical Research Letters},
  year={1999},
  volume={6},
  pages={573-580}
}
  • Florin Ambro
  • Published 13 June 1999
  • Mathematics
  • Mathematical Research Letters
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 semi-continuity behaviour for varieties of dimension at most 3 and for toric varieties of arbitrary dimension. 
Minimal log discrepancies in positive characteristic
Abstract 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
Minimal log discrepancies of regularity one
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
On semi-continuity problems for minimal log discrepancies
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
On minimal log discrepancies on varieties with fixed Gorenstein index
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
LETTERS OF A BI-RATIONALIST IV. Geometry of log flips
For a birational log Fano contraction, it is conjectured an inequality between the dimension of its exceptional locus and the minimal log discrepancy over the locus. The conjecture follows from the
Boundedness of $\epsilon$-log Canonical Complements on Surfaces
We prove a conjecture due to V.V. Shokurov on the boundedness of $\epsilon$-log canonical complements on surfaces. As an application we give a new proof to the boundedness of weak log Fano surfaces.
The ACC Conjecture for minimal log discrepancies on a fixed germ
We show that on a klt germ (X,x), for every finite set I there is a positive integer N with the following property: for every R-ideal J on X with exponents in I, there is a divisor E over X that
On minimal log discrepancies and kollár components
  • Joaqu'in Moraga
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2021
In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$ -dimensional $a$ -log canonical singularities with standard
On generalized minimal log discrepancy
We discuss the ACC conjecture and the LSC conjecture for minimal log discrepancies of generalized pairs. We prove that some known results on these two conjectures for usual pairs are still valid for
A boundedness conjecture for minimal log discrepancies on a fixed germ
We consider the following conjecture: on a klt germ (X,x), for every finite set I there is a positive integer N with the property that for every R-ideal J on X with exponents in I, there is a divisor
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 39 REFERENCES
Minimal discrepancies of toric singularities
The main purpose of this paper is to prove that minimal discrepancies ofn-dimensional toric singularities can accumulate only from above and only to minimal discrepancies of toric singularities of
Log canonical singularities and complete moduli of stable pairs
1) Assuming log Minimal Model Conjecture, we give a construction of a complete moduli space of stable log pairs of arbitrary dimension generalizing directly the space M_{g,n} of pointed stable
Minimal Discrepancy for a Terminal cDV Singularity Is 1
An answer to a question raised by Shokurov on the minimal discrepancy of a terminal singularity of index 1 is given. It is proved that the minimal discrepancy is 1 (it is 2 for a non-singular point
The Adjunction Conjecture and its applications
We discuss adjunction formulas for fiber spaces and embeddings, extending the known results along the lines of the Adjunction Conjecture, independently proposed by Y. Kawamata and V.V. Shokurov. As
Two two-dimensional terminations
Varieties with log terminal and log canonical singularities are considered in the Minimal Model Program, see \cite{...} for introduction. In \cite{shokurov:hyp} it was conjectured that many of the
3-FOLD LOG FLIPS
We prove that 3-fold log flips exist. We deduce the existence of log canonical and -factorial log terminal models, as well as a positive answer to the inversion problem for log canonical and log
On $3$-dimensional terminal singularities
Canonical and terminal singularities are introduced by M. Reid [5], [6]. He proved that 3-dimensional terminal singularities are cyclic quotient of smooth points or cDV points [6].
Introduction to Toric Varieties.
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic
Flip theorem and the existence of minimal models for 3-folds
§ O. Introduction § I. Preliminaries and basic definitions § la (Appendix la). Results on 3-fold terminal singularities § Ib (Appendix Ib). Deformation of extremal nbds § 2. Numerical invariants
Singularities of Pairs
These are the revised notes of my lectures at the 1995 Santa Cruz summer institute. Changes from the Jan.26,1996 version: Major: 7.1--2; Medium: 3.7, 3.11, 5.3.3, 7.9.2, 9.8.
...
1
2
3
4
...