Geodesic
On K\"uchle varieties with Picard number greater than~1
Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 698-709

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We describe the geometry of Küchle varieties (that is, Fano fourfolds of index 1 contained in Grassmannians as zero loci of sections of equivariant vector bundles) with Picard number greater than 1. We also describe the structure of their derived categories.
Keywords: Fano varieties, special varieties, semiorthogonal decompositions of derived categories. 
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     author = {A. G. Kuznetsov},
     title = {On {K\"uchle} varieties with {Picard} number greater than~1},
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A. G. Kuznetsov. On K\"uchle varieties with Picard number greater than~1. Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 698-709. http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a2/