1998/05/26 by A. A'Campo-Neuen, J. Hausen
Mathematics · #math.AG #msc:14M25 #msc:14L30 #msc:14D25
published as Math. Z. 233, 697-708 (2000) · 12 pages, 3 figures, LaTeX2e + Postscript
arxiv created 1998/05/26 · arxiv updated 2009/11/30
We 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.