2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131852We study global log canonical thresholds on anticanonically embedded quasismooth weighted Fano threefold hypersurfaces having terminal quotient singularities to prove the existence of a Kahler-Einstein metric on most of them, and to produce examples of Fano varieties with infinite discrete groups of birational automorphisms.short version, 19 pages, to appear in Advances in MathematicsAlgebraic Geometry14E05, 14E07, 14E08, 14J45, 14Q10, 32Q20text