Geodesic
On the existence of complements of the~canonical divisor for Mori conic bundles
Sbornik. Mathematics, Tome 188 (1997) no. 11, pp. 1665-1685

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This paper continues the author's study of extremal contractions in the sense of Mori from three-dimensional varieties onto surfaces. Such contractions occur in a natural way in the birational classification theory of three-dimensional algebraic varieties. Reid's “general elephant” conjecture of the complementedness of the canonical divisor and also the conjecture about singularities of the base surface are discussed. The situation is studied locally near a singular fibre. 
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     author = {Yu. G. Prokhorov},
     title = {On the existence of complements of the~canonical divisor for  {Mori} conic bundles},
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     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_11_a3/}
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Yu. G. Prokhorov. On the existence of complements of the~canonical divisor for  Mori conic bundles. Sbornik. Mathematics, Tome 188 (1997) no. 11, pp. 1665-1685. http://geodesic.mathdoc.fr/item/SM_1997_188_11_a3/