2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67183We describe the set of Mori structures for a Fano 3-fold of index 2 and degree 1 (the double cone over the Veronese surface). In partiular, it is proved that such a Fano variety is not rational, the group of birational automorphisms coincides with the group of biregular automorphisms, and there are no structures of conic bundle.24 pages, 3 figuresAlgebraic Geometry14E07; 14E08text