# 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.

#### One Citation

Strong $(\delta,n)$-complements for semi-stable morphisms

- Mathematics
- 2018

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 strong… Expand

#### References

SHOWING 1-10 OF 18 REFERENCES

Complements on surfaces

- Mathematics
- 1997

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 for… Expand

Lectures on complements on log surfaces

- Mathematics
- 2001

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

- Mathematics
- 2004

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 one… Expand

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

- Mathematics
- 1998

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

- Mathematics
- 2002

We classify logarithmic Enriques surfaces with δ= 2

3-FOLD LOG FLIPS

- Mathematics
- 1993

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… Expand

Classification of three-dimensional exceptional log canonical hypersurface singularities. II

- Mathematics
- 2002

We describe three-dimensional exceptional strictly log canonical hypersurface singularities and give a detailed classification of three-dimensional exceptional canonical hypersurface singularities… Expand

Rational curves on quasi-projective surfaces

- Mathematics
- 1997

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 to… Expand

Boundedness of non-birational extremal contractions

- Mathematics
- 1999

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