2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76966We define a quasi--projective reduction of a complex algebraic variety $X$ to be a regular map from $X$ to a quasi--projective variety that is universal with respect to regular maps from $X$ to quasi--projective varieties. A toric quasi--projective reduction is the analogous notion in the category of toric varieties. For a given toric variety $X$ we first construct a toric quasi--projective reduction. Then we show that $X$ has a quasi--projective reduction if and only if its toric quasi--projective reduction is surjective. We apply this result to characterize when the action of a subtorus on a quasi--projective toric variety admits a categorical quotient in the category of quasi--projective varieties.12 pages, 3 figures, LaTeX2e + PostscriptAlgebraic Geometry14M25, 14L30, 14D25text