2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66286We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant Fano compactification G/H there exists.10 pages, 1 figureAlgebraic GeometryRepresentation Theory14J45, 14E30text