Related papers: Automorphisms of unstable ${\mathbb P}^1$-bundles

For a homeomorphism $T \colon X \to X$ of a compact metric space $X$, the stabilized automorphism group $\text{Aut}^{(\infty)}(T)$ consists of all self-homeomorphisms of $X$ which commute with some power of $T$. Motivated by the study of…

Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial…

An automorphism $\alpha$ of a group $G$ is normal if it fixes every normal subgroup of $G$ setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively…

Consider a polynomial F such that each variable appears in exactly one monomial. The hypersurface defined by the polynomial F is called a hypersurface with separable variables. A variety is called rigid if there are no nontrivial actions of…

Given a connected reductive algebraic group $G$ and a spherical $G$-variety $X$, a $B$-root subgroup on $X$ is a one-parameter additive group of automorphisms of $X$ normalized by a Borel subgroup $B \subset G$. We obtain a complete…

If G is a non-cyclic finite group, non-isomorphic G-sets X, Y may give rise to isomorphic permutation representations C[X] and C[Y]. Equivalently, the map from the Burnside ring to the representation ring of G has a kernel. Its elements are…

Let $\pi :X\rightarrow \mathbb{P}^3$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then its first and second dynamical degrees are the same. We also construct many…

Let $k$ be an algebraically closed field of positive characteristic $p>0$ and $C \to {\mathbb P}^1_k$ a $p$-cyclic cover of the projective line ramified in exactly one point. We are interested in the $p$-part of the full automorphism group…

In the paper autonilpotent groups were characterized as groups $G$ such that $\mathrm{Aut}G$ stabilizes some chain of subgroups of $G$. It was shown that a $p$-group is autonilpotent if and only if its group of automorphisms is also a…

Let $\overline G$ be the wonderful compactification of a simple affine algebraic group $G$ defined over $\mathbb C$ such that its center is trivial and $G\not= {\rm PSL}(2,\mathbb{C})$. Take a maximal torus $T \subset G$, and denote by…

Let G be a connected reductive complex algebraic group acting on a smooth complete complex algebraic variety X. We assume that X under the action of G is a regular embedding, a condition satisfied in particular by smooth toric varieties and…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

A loop $(X,\circ)$ is said to be a Bruck loop if it satisfies the (right) Bol identity $((z\circ x)\circ y)\circ x = z\circ ((x\circ y)\circ x)$ and the automorphic inverse property $(x\circ y)^{-1}=x^{-1}\circ y^{-1}$. If $X$ is a finite…

It is well known that not every finite group arises as the full automorphism group of some group. Here we show that the situation is dramatically different when considering the category of partial groups, ${{\mathcal P}art}$, as defined by…

We study Fell bundles on groupoids from the viewpoint of quantale theory. Given any saturated upper semicontinuous Fell bundle $\pi:E\to G$ on an \'etale groupoid $G$ with $G_0$ locally compact Hausdorff, equipped with a suitable completion…

An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. The group ring $RG$ of a finite group $G$ is isomorphic to the set of {\em group ring matrices} over $R$. It is shown that…

Let $X$ be a compact Riemann surface of genus $g\geq 2$. Let $Aut(X)$ be its group of automorphisms and $G\subseteq Aut(X)$ a subgroup. Sharp upper bounds for $|G|$ in terms of $g$ are known if $G$ belongs to certain classes of groups, e.g.…

Let $X$ be a perfectoid space with tilt $X^\flat$. We construct a canonical map $\theta:\operatorname{Pic} X^\flat\to\lim\operatorname{Pic} X$ where the (inverse) limit is taken over the $p$-power map, and show that $\theta$ is an…

A closed subgroup of a semisimple algebraic group is called irreducible if it lies in no proper parabolic subgroup. In this paper we classify all irreducible $A_1$ subgroups of exceptional algebraic groups $G$. Consequences are given…

Let $G$ be a connected semisimple algebraic group of adjoint type over the field $\mathbb{C}$ of complex numbers and $B$ be a Borel subgroup of $G.$ Let $F$ be an irreducible projective $B$-variety. Then consider the variety…