Related papers: On automorphisms of flexible varieties

Let $k$ be an algebraically closed field of characteristic zero. Let $S$ be a smooth projective variety over $k$ and let $p_S:X\rightarrow S$ be a family of smooth projective curves over $S$. Let $E$ be a vector bundle over $X$. For $s\in…

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…

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

We determine the geometric structure of a minimal projective threefold having two `independent and commutative' automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X, G). As…

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all…

An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…

For a surjective self-morphism on a projective variety defined over a number field, we study the preimages question, which asks if the set of rational points on the iterated preimages of an invariant closed subscheme eventually stabilize.…

We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…

A bounded automorphism of a field or a group with trivial approximate centre is definable. In an expansion of a field by a Pfaffian family F of additive endomorphisms such that algebraic closure in the expansion coincides with relative…

Let K be an algebraically closed field of characteristic zero. We show that if the automorphisms group of a quasi-affine variety X is infinite, then X is uniruled.

Trinomial varieties are affine varieties given by some special system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal rational varieties with torus action of complexity one. For…

An affine variety $X$ of dimension $\ge 2$ is called {\em flexible} if its special automorphism group SAut$(X)$ acts transitively on the smooth locus $X_{reg}$ \cite{AKZ}. Recall that the special automorphism group SAut$(X)$ is the subgroup…

Let $k$ be a field, $X$ a connected scheme proper over $k$, $D\subsetneq X$ an ample effective connected divisor, $x\in D(k)$. For Tannakian categories $\mathcal{C}_X$ and $\mathcal{C}_D$ whose objects consist of vector bundles on $X$ and…

Let $A$ be an Azumaya algebra over a field. If $G$ is the group of automorphisms of $A$ and $X$ denotes a projective homogeneous variety under $G$, we construct in a very explicit way and under suitable hypotheses a bundle $\mathcal{V}$ on…

Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field $\mathbb F_2$ (with respect to all $\mathbb F_2$-algebra automorphisms) are fully described.

We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the…

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

We describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero.

We show that if g is a generic (in the sense of Baire category) isometry of a generic subspace of the Urysohn metric space U, then g does not extend to a full isometry of U. The same holds for the Urysohn sphere S. Let M be a Fraisse…