Complements on log surfaces

@article{Kudryavtsev2004ComplementsOL,
  title={Complements on log surfaces},
  author={S. Kudryavtsev},
  journal={Sbornik Mathematics},
  year={2004},
  volume={195},
  pages={859-878}
}
The main inductive theorem on complements on surfaces is refined and models for exceptional log del Pezzo surfaces with δ = 0 are constructed. Bibliography: 18 titles. 
1 Citations

Figures from this paper

Strong $(\delta,n)$-complements for semi-stable morphisms
We prove boundedness of global strong $(\delta,n)$-complements for generalized $\epsilon$-log canonical pairs of Fano type. We also prove some partial results towards boundedness of local strongExpand

References

SHOWING 1-10 OF 18 REFERENCES
Complements on surfaces
The main result is a boundedness theorem forn-complements on algebraic surfaces. In addition, this theorem is used in a classification of log Del Pezzo surfaces and birational contractions forExpand
Lectures on complements on log surfaces
The aim of these notes is to explain main ideas of the theory of complements. Basically we will follow Shokurov's work alg-geom/9711024.
Q-complements on log surfaces
In this paper the log surfaces without $\QQ$-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows oneExpand
Classification of Exceptional Log Del Pezzo Surfaces with Δ = 1
The exceptional log Del Pezzo surfaces with δ = 1 are classified.
Mori conic bundles with a reduced log-terminal boundary
We study the local structure of Mori contractionsf:X→Z of relative dimension one under an additional assumption that there exists a reduced divisorS such thatKx+S is plt and anti-ample.
Classification of Logarithmic Enriques Surfaces with δ=2
We classify logarithmic Enriques surfaces with δ= 2
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 logExpand
Classification of three-dimensional exceptional log canonical hypersurface singularities. II
We describe three-dimensional exceptional strictly log canonical hypersurface singularities and give a detailed classification of three-dimensional exceptional canonical hypersurface singularitiesExpand
Rational curves on quasi-projective surfaces
Introduction and statement of results Glossary of notation and conventions Gorenstein del Pezzo surfaces Bug-eyed covers Log deformation theory Criteria for log uniruledness Reduction toExpand
Boundedness of non-birational extremal contractions
We consider $K_X$-negative extremal contractions $f\colon X\to (Z,o)$, where $X$ is an algebraic threefold with only $\epsilon$-log terminal Q-factorial singularities and $(Z,o)$ is a two (resp.,Expand
...
1
2
...