Related papers: On the automorphism groups of certain branched str…

In this paper, we prove that each automorphism of the Torelli group of a surface is induced by a diffeomorphism of the surface, provided that the surface is a closed, connected, orientable surface of genus at least 3. This result was…

We classify Coble surfaces with finite automorphism group in arbitrary characteristic not equal to 2. There are exactly 9 isomorphism classes of such surfaces.

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group $G$ there are infinitely many isomorphism classes of compact complex hyperbolic $2$-manifolds with automorphism group isomorphic to…

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.

We study the automorphism group of graphons (graph limits). We prove that after an appropriate "standardization" of the graphon, the automorphism group is compact. Furthermore, we characterize the orbits of the automorphism group on…

Given a pair of translation surfaces it is very difficult to determine whether they are supported on the same algebraic curve. In fact, there are very few examples of such pairs. In this note we present infinitely many examples of finite…

We show that the extended based mapping class group of an infinite-type surface is naturally isomorphic to the automorphism group of the loop graph of that surface. Additionally, we show that the extended mapping class group stabilizing a…

We prove that the automorphism groups of simple polarized abelian varieties of odd prime dimension over finite fields are cyclic, and give a complete list of finite groups that can be realized as such automorphism groups.

We prove that, except in certain low-complexity cases, the automorphism group of the graph of pants decompositions of a nonorientable surface is isomorphic to the mapping class group of that surface.

We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang's conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

We study automorphism groups of real del Pezzo surfaces, concentrating on finite groups acting minimally on them. As a result, we obtain a vast part of classification of finite subgroups in the real plane Cremona group.

Frucht showed that, for any finite group $G$, there exists a cubic graph such that its automorphism group is isomorphic to $G$. For groups generated by two elements we simplify his construction to a graph with fewer nodes. In the general…

We prove some general results concerning the size of the group of automorphisms of the Douady space of points on a surface. We then study some properties of the automorphisms coming from an automorphism of the surface, in particular their…

We discuss the possibility of lifting finite subgroups, and in particular finite cyclic subgroups, with respect to the canonical projections between automorphism and outer automorphism groups of free groups, surface groups and their…

We construct k-parameter families of rational surface automorphisms for any k. These are automorphisms of surfaces X, which are constructed from iterated blowups over the projective plane. In certain cases: we are able to determine the…

In this paper we introduce, for each closed orientable surface, an analogue of Tits buildings adjusted to investigation of the Torelli group of this surface. It is a simplicial complex with some additional structure. We call this complex…

We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.

Let $p:\Sigma'\to\Sigma$ be a finite Galois cover, possibly branched, with Galois group $G$. We are interested in the structure of the cohomology of $\Sigma'$ as a module over $G$. We treat the cases of branched and unbranched covers…