7 papers · 1 filter
Orbit spaces of small tori
A. A'Campo-Neuen, J. Hausen
Consider an algebraic torus of small dimension acting on an open subset of a complex vector space, or more generally on a quasiaffine variety such that a separated orbit space exis…
Homogeneous Coordinates and Quotient Presentations for Toric Varieties
A. A'Campo-Neuen, J. Hausen, S. Schroeer
Generalizing cones over projective toric varieties, we present arbitrary toric varieties as quotients of quasiaffine toric varieties. Such quotient presentations correspond to grou…
Examples and Counterexamples for Existence of Categorical Quotients
A. A'Campo-Neuen, J. Hausen
We give examples for existence and non-existence of categorical quotients for algebraic group actions in the categories of algebraic varieties and prevarieties. All our examples ar…
Quotients of Divisorial Toric Varieties
A. A'Campo-Neuen, J. Hausen
We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characteriz…
Toric Prevarieties and Subtorus Actions
A. A'Campo-Neuen, J. Hausen
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 geom…
Quotients of Toric Varieties by the Action of a Subtorus
A. A'Campo-Neuen, J. Hausen
We consider the action of a subtorus of the big torus on a toric variety. The aim of the paper is to define a natural notion of a quotient for this setting and to give an explicit…