Flexible varieties and automorphism groups

Given an irreducible affine algebraic variety X of dimension n≥2 , we let SAut(X) denote the special automorphism group of X , that is, the subgroup of the full automorphism group Aut(X) generated by all one-parameter unipotent subgroups. We show that if SAut(X) is transitive on the smooth locus X reg , then it is infinitely transitive on X reg . In turn, the transitivity is equivalent to the flexibility of X . The latter means that for every smooth point x∈X reg the tangent space T x X is spanned by the velocity vectors at x of one-parameter unipotent subgroups of Aut(X) . We also provide various modifications and applications.

Perceived Competition Explains Regional Differences in the Stereotype Content of Immigrant Groups

This research investigates differences in the stereotype content of immigrant groups between linguistic regions. We expected that immigrant groups who speak the local language of a specific linguistic region would be perceived as more competitive within this region than in another linguistic region. Further, we expected these differences would underlie regional differences in stereotype content, albeit only for the warmth dimension. Predictions were tested in the two largest linguistic regions of Switzerland. As expected, in the German-speaking region, locals perceived German immigrants as more competitive and thus as less warm, whereas in the French-speaking region, locals perceived French immigrants as more competitive and, consequently, as less warm. So, paradoxically, immigrants with strong integration potential are particularly disliked because they are regarded as direct competitors.

Lipschitz extensions of maps between Heisenberg groups

Let $\H^n$ be the Heisenberg group of topological dimension 2n+1 . We prove that if n is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension property.