Geodesic
$\mathbb Q$-Complements on Log Surfaces
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 181-182 
S. A. Kudryavtsev; I. Yu. Fedorov. $\mathbb Q$-Complements on Log Surfaces. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic geometry: Methods, relations, and applications, Tome 246 (2004), pp. 181-182. http://geodesic.mathdoc.fr/item/TM_2004_246_a12/
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     author = {S. A. Kudryavtsev and I. Yu. Fedorov},
     title = {$\mathbb Q${-Complements} on {Log} {Surfaces}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Log surfaces without $\mathbb Q$-complement are classified.

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[2] Kudryavtsev S. A., Complements on log surfaces, , 2003 arXiv: /math.AG/0304437 | MR

[3] Prokhorov Yu. G., Lectures on complements on log surfaces, MSJ Memoirs, 10, Math. Soc. Japan, Tokyo, 2001 | MR

[4] Hartshorne R., Algebraic geometry, Springer, New York, 1977 | MR | Zbl

[5] Shokurov V. V., “Complements on surfaces”, J. Math. Sci., 102:2 (2000), 3876–3932 | DOI | MR | Zbl