Search results for "Algebraic torus"

showing 2 items of 2 documents

Actions de tores algébriques sur des corps de caractéristique zéro

2023

Over an algebraically closed field of characteristic zero, normal affine varieties endowed with an effective torus action were described by Altmann and Hausen in 2006 by a geometrico-combinatorial presentation.Using Galois descent tools, we extend this presentation to the case where the ground field is an arbitrary field of characteristic zero. In this context, the acting torus may be non split and may have non-trivial torsors, thus we need additional data to encode such varieties. We provide some situations where the generalized Altmann-Hausen presentation simplifies. For instance, if the acting torus is split, we recover mutatis mutandis the original Altmann-Hausen presentation. Finally, …

Convex geometryAction of algebraic torusActions de tores algébriquesStructures et formes réellesGéométrie birationnelle[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Birational geometryGéométrie convexeReal structures and real forms
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Orbit spaces of Small Tori

2003

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.

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