Quasi--Projective Reduction of Toric Varieties

Details Quasi--Projective Reduction of Toric Varieties Quasi--Projective Reduction of Toric Varieties

1998-05-26

arxiv.org/abs/math/9805118v1

Math. Z. 233, 697-708 (2000)

Mathematics

Algebraic Geometry

12 pages, 3 figures, LaTeX2e + Postscript

Scientific paper

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.

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