Geodesic
Hyperelliptic and trigonal Fano threefolds
Izvestiya. Mathematics , Tome 69 (2005) no. 2, pp. 365-421

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We classify Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system has no base points but does not give an embedding, and we classify anticanonically embedded Fano 3-folds with canonical Gorenstein singularities which are not intersections of quadrics. We also study rationality questions for most of these varieties. 
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     author = {V. V. Przyjalkowski and I. A. Cheltsov and K. A. Shramov},
     title = {Hyperelliptic and trigonal {Fano} threefolds},
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V. V. Przyjalkowski; I. A. Cheltsov; K. A. Shramov. Hyperelliptic and trigonal Fano threefolds. Izvestiya. Mathematics , Tome 69 (2005) no. 2, pp. 365-421. http://geodesic.mathdoc.fr/item/IM2_2005_69_2_a4/