Toric Prevarieties and Subtorus Actions
| dc.creator | A'Campo-Neuen, A. | |
| dc.creator | Hausen, J. | |
| dc.date | 1999-12-30 | |
| dc.date.accessioned | 2026-07-07T05:32:33Z | |
| dc.date.available | 2026-07-07T05:32:33Z | |
| dc.description | Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the category of toric prevarieties in terms of convex-geometrical data, so-called systems of fans. In a second part, we consider actions of subtori H of the big torus of a toric prevariety X and investigate quotients for such actions. Using our language of systems of fans, we characterize existence of good prequotients for the action of H on X. Moreover, we show by means of an algorithmic construction that there always exists a toric prequotient for the action of H on X, that means an H-invariant toric morphism p from X to a toric prevariety Y such that every H-invariant toric morphism from X to a toric prevariety factors through p. Finally, generalizing a result of D. Cox, we prove that every toric prevariety occurs as the image of a categorical prequotient of an open toric subvariety of some complex affine space. | |
| dc.description | 24 pages, 5 figures, LaTeX2e+pstex | |
| dc.identifier | https://arxiv.org/abs/math/9912229 | |
| dc.identifier | http://arxiv.org/abs/math/9912229 | |
| dc.identifier | Geometriae Dedicata 87, 35-64 (2001) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79694 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L30; 14M25 | |
| dc.title | Toric Prevarieties and Subtorus Actions | |
| dc.type | text |