Quasi-projective reduction of toric varieties |
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Authors: | A A'Campo–Neuen J Hausen |
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Institution: | Fakult?t für Mathematik und Informatik, Universit?t Konstanz Fach D197, D–78457 Konstanz, Germany e-mail: Annette.ACampo@uni-konstanz.de, Juergen.Hausen@uni-konstanz.de, DE
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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.
Received October 29, 1998; in final form December 28, 1998 |
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