6533b7d9fe1ef96bd126d2fb
RESEARCH PRODUCT
Actions de tores algébriques sur des corps de caractéristique zéro
Pierre-alexandre Gillardsubject
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 formsdescription
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, we focus on the real setting and on affine varieties endowed with a two-dimensional torus action. In the latter case we relate the torsor appearing in the generalized Altmann-Hausen presentation to some smooth toric Del Pezzo surface.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2023-01-01 |