2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64176In this paper, we obtain a complete classification of smooth toric Fano varieties equipped with extremal contractions which contract divisors to curves for any dimension. As an application, we obtain a complete classification of smooth projective toric varieties which can be equivariantly blown-up to Fano along curves.14 pages, Latex2eAlgebraic Geometry14M25; 14E30, 14J45text