On the Picard Number of Fano 3-Folds with Terminal Singularities

Details On the Picard Number of Fano 3-Folds with Terminal Singularities On the Picard Number of Fano 3-Folds with Terminal Singularities

1993-11-19

arxiv.org/abs/alg-geom/9311007v1

Mathematics

Algebraic Geometry

35 pages, AMS-Tex, version 2.1, Preprint MSRI Berkeley, June 057-93 (corrected variant)

Scientific paper

We prove the following main result: Let X be a Fano 3-fold with terminal
Q-factorial singularities and X does not have a small extremal ray and a face
of Kodaira dimension 1 or 2 for Mori polyhedron of X. Then the Picard number
\rho (X) < 8.

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