Quasi--Projective Reduction of Toric Varieties

A. A'Campo-Neuen; J. Hausen

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arXiv · math/9805118

Quasi--Projective Reduction of Toric Varieties

A. A'Campo-Neuen·J. Hausen

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Abstract

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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BibTeX RIS

A. A'Campo-Neuen, J. Hausen. 1998-05-26. Quasi--Projective Reduction of Toric Varieties. https://arxiv.org/abs/math/9805118

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