Search results for "group actions"
showing 6 items of 6 documents
Proper triangular Ga-actions on A^4 are translations
2013
We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3.
Rationally integrable vector fields and rational additive group actions
2016
International audience; We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar-Limanov invariant…
The varieties of bifocal Grassmann tensors
2022
AbstractGrassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann…
Hyperbolicity as an obstruction to smoothability for one-dimensional actions
2017
Ghys and Sergiescu proved in the $80$s that Thompson's group $T$, and hence $F$, admits actions by $C^{\infty}$ diffeomorphisms of the circle . They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of piecewise projective homeomorphisms, and Lodha-Moore defined finitely presentable groups of piecewise projective homeomorphisms. These groups are of particular interest because they are nonamenable and contain no free subgroup. In contrast to the result of Ghys-Sergiescu, we prove that the groups of Monod and Lodha-Moore are not topologically conjugate to a group of $C^1$ diffeomorphisms. Fur…
homogeneous embeddings of SL2(C) modulo a finite sub-group.
2000
L'objet de ce travail est l'étude des variétés algébriques normales complexes munies d'une action algébrique de $SL_{2}$ et qui contiennent $SL_{2}/H$ comme orbite ouverte, $H$ étant un sous-groupe fini de $SL_{2}$.Plus précisément on définit un plongement homogène de $SL_{2}/H$ comme la donnée d'une $SL_{2}$-variété irréductible $X$ (quasi-projective ou non) contenant $SL_{2}/H$ comme orbite ouverte et d'un morphisme $SL_{2}$-équivariant de $SL_{2}$ dans $X$.Les plongements homogènes lisses ainsi que les plongements minimaux (plongements lisses et complets qui ne sont pas des éclatements d'un autre plongement lisse complet) de $SL_{2}/\{Id\}$ et de $SL_{2}/\{\pm Id\}$ ont été déterminés pa…