ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14E30 Prokhorov, Yuri G., Moscow State University Mori contractions of relative dimension 1 A Mori conic bundle is an extremal contraction from a threefold with only terminal singularities onto a surface (see [1]). We give a partial classification of such contractions and prove that the canonical divisor is n-complementary (in the sense of [2]) for bounded n. Connections with blow-ups of terminal singularities are discussed. References:

[1] Yu. G. Prokhorov, On the existence of complements of canonical divisor for Mori conic bundles, Russian Acad. Sci. Sb. Math. 188 (1997), 99–120.

[2] V. V. Shokurov,3-fold log flips, Russian Acad. Sci. Izv. Math. 40 (1993), 93–202 & 43 (1994), 527–558.