6533b82ffe1ef96bd12964b7

RESEARCH PRODUCT

Orbit spaces of Small Tori

Annette A’campo-neuenJuergen Hausen

subject

Pure mathematicsMathematics::Commutative AlgebraApplied MathematicsMathematical analysisToric varietyTorusAlgebraic geometryMathematics::Algebraic GeometryMathematics (miscellaneous)Algebraic torusInvariant (mathematics)Mathematics::Symplectic GeometryMathematicsCounterexample

description

Consider an algebraic torus of small dimension acting on an open subset of ℂn, or more generally on a quasiaffine variety such that a separated orbit space exists. We discuss under which conditions this orbit space is quasiprojective. One of our counterexamples provides a toric variety with enough effective invariant Cartier divisors that is not embeddable into a smooth toric variety.

https://doi.org/10.1007/bf03322717