Related papers: Infinite transitivity for Calogero-Moser spaces

Let G be the group of symplectic (unimodular) automorphisms of the free associative algebra on two generators. A theorem of G.Wilson and the first author asserts that G acts transitively the Calogero-Moser spaces C_n for all n. We…

Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. If $M$ is connected and $\dim(M)\geq 2$, the group of diffeomorphisms of $M$, that are isotopic to the identity through a compactly supported isotopy, acts $n$-transitively…

A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to two, we show that, under a mild restriction,…

We prove the algebraic density property for the Calogero--Moser spaces $\mathcal{C}_{n}$, and give a description of the identity component of the group of holomorphic automorphisms of $\mathcal{C}_{n}$.

For a Calabi-Yau manifold $X$, the Kawamata - Morrison movable cone conjecture connects the convex geometry of the movable cone $\overline{\mathrm{Mov}}(X)$ to the birational automorphism group. Using the theory of Coxeter groups, Cantat…

In this paper, we classify the $m$-ovoids of finite classical polar spaces that admit a transitive automorphism group acting irreducibly on the ambient vector space. In particular, we obtain several new infinite families of transitive…

We prove that every irreducible component of the fixed point variety under the action of $d$-th roots of unity in a smooth Caloger-Moser space is isomorphic to a Calogero-Moser space associated with another reflection group.

Let X be an algebraic variety covered by open charts isomorphic to the affine space and q: X' \to X be the universal torsor over X. We prove that the automorphism group of the quasiaffine variety X' acts on X' infinitely transitively. Also…

It is known that if the special automorphism group $\text{SAut}(X)$ of a quasiaffine variety $X$ of dimension at least $2$ acts transitively on $X$, then this action is infinitely transitive. In this paper we address the question whether…

We prove that for many pairs $H_1, H_2$ of root subgroups of the automorphism group $\text{Aut}(\mathbb{C}^2)$ the diagonal action of the group generated by $H_1, H_2$ on $(\mathbb{C}^2)^m$ has an open orbit for any positive integer $m$.…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

We introduce the symplectic holomorphic density property and the Hamiltonian holomorphic density property together with the corresponding version of Anders\'en-Lempert theory. We establish these properties for the Calogero-Moser space…

We prove that the action of the semigroup generated by a $C^r$ generic pair of area-preserving diffeomorphisms of a compact orientable surface is transitive.

Some groups of real analytic diffeomorphism act n-transitively for each finite n.

The real Calogero--Moser space $\mathcal{C}_n^\mathbb{R}$ is a noncompact, totally real submanifold of the complex Calogero--Moser space $\mathcal{C}_n$. We prove that every symplectic diffeomorphism of $\mathcal{C}_n^\mathbb{R}$ smoothly…

In this short note, we prove the existence of infinitely many pairwise non-isomorphic non-hyperelliptic Riemann surfaces with automorphism group acting transitively on the Weierstrass points. We also found all those compact Riemann surfaces…

The notion of $n$-transitivity can be carried over from groups of diffeomorphisms on a manifold $M$ to groups of bisections of a Lie groupoid over $M$. The main theorem states that the $n$-transitivity is fulfilled for all $n\in\mathbb N$…

Moser's theorem (1965) states that the diffeomorphism group of a compact manifold acts transitively on the space of all smooth positive densities with fixed volume. Here we describe the extension of this result to manifolds with corners. In…

We define a tracelike transformation to be a natural family of conjugation invariant maps $T_{x,C}: hom_C(x,x) \to hom_C(1,1)$ for all dualisable objects $x$ in any symmetric monoidal infinity-category $C$. This generalises the trace from…

We describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra $ A_1 $. In particular, we give a geometric presentation for these groups in terms of amalgamated products, using the Bass-Serre…