Two two-dimensional terminations

@article{Alexeev1992TwoTT,
  title={Two two-dimensional terminations},
  author={Valery Alexeev},
  journal={Duke Mathematical Journal},
  year={1992},
  volume={69},
  pages={527-545}
}
  • V. Alexeev
  • Published 12 June 1992
  • Mathematics
  • Duke Mathematical Journal
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 interesting sets, associated with these varieties have something in common: they satisfy the ascending chain condition, which means that every increasing chain of elements terminates. Philosophically, this is the reason why two main hypotheses in the Minimal Model Program: existence and termination of… 

Figures from this paper

Boundedness of ǫ-lc Complements on Surfaces
Contents 1 Boundedness of ǫ-log canonical complements on surfaces 2 1. 1 Boundedness of ǫ-log canonical complements on surfaces 1.1 Introduction The concept of complement was introduced and studied
On a conjecture of Shokurov: characterization of toric varieties
We verify a special case of V. V. Shokurov's conjecture about characterization of toric varieties. More precisely, let $(X,D=\sum d_iD_i)$ be a three-dimensional log variety such that $K_X+D$ is
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
Algebraic Surfaces with Log-Terminal Singularities and nef Anticanonical Class and Reflection Groups in Lobachevsky Spaces. I (Basics of the Diagram Method)
In our preprint: "Algebraic surfaces with log-terminal singularities and nef anticanonical class and reflection groups in Lobachevsky spaces", Preprint Max-Planck-Institut f\"ur Mathematik, Bonn,
Bounding singular surfaces via Chern numbers
We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and Chern numbers. As an application, we prove that given $$R\in
Mld's vs thresholds and flips
Abstract Minimal log discrepancies (mld's) are related not only to termination of log flips [Shokurov, Algebr. Geom. Metody 246: 328–351, (2004)] but also to the ascending chain condition (ACC) of
Descending chain condition for stringy invariants (Higher Dimensional Algebraic Geometry)
It is known that the degree of the stringy \mathrm{E}‐function of a \log terminal singularity is related to the minimal log discrepancy, and the minimal \log discrepancies of certain classes of
On numerical nonvanishing for generalized log canonical pairs.
The nonvanishing conjecture for projective log canonical pairs plays a key role in the minimal model program of higher dimensional algebraic geometry. The numerical nonvanishing conjecture considered
Log canonical $3$-fold complements
We expand the theory of log canonical $3$-fold complements. More precisely, fix a set $\Lambda \subset \mathbb{Q}$ satisfying the descending chain condition with $\overline{\Lambda} \subset
Limits of log canonical thresholds
Let Tn denote the set of log canonical thresholds of pairs (X, Y ), with X a nonsingular variety of dimension n, and Y a nonempty closed subscheme of X. Using non-standard methods, we show that every
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 16 REFERENCES
Threefolds whose canonical bundles are not numerically effective.
  • S. Mori
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1980
TLDR
A characterization of an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective and which contains an exceptional divisor of several types, which is classified explicitly.
ON THE CLOSED CONE OF CURVES OF ALGEBRAIC 3-FOLDS
In this paper the author establishes, under natural conditions, the local polyhedrality of the closed cone of curves of a three-dimensional algebraic variety in the part that is negative with respect
FRACTIONAL INDICES OF LOG DEL PEZZO SURFACES
The fractional index of a (possibly singular) -Gorenstein del Pezzo surface  is the greatest rational number  such that , where  is a primitive Cartier divisor. This paper describes the set of values
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
Log Del Pezzo surfaces III. Math. USSR Izvestia
  • Log Del Pezzo surfaces III. Math. USSR Izvestia
  • 1990
Classification of Del Pezzo surfaces with log terminal singularities of index ≤ 2 and involutions on K3 surfaces
  • Soviet Math. Dokl. 39
  • 1989
Ann of Math
  • Ann of Math
  • 1988
In: Birational geometry of algebraic varieties: open problems. 23 Taneguchi intnl symposium
  • In: Birational geometry of algebraic varieties: open problems. 23 Taneguchi intnl symposium
  • 1988
...
1
2
...