Related papers: Fuchsian affine actions of surface groups

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic…

We show that the generic fiber of a family of smooth $\mathbb{A}^{1}$-ruled affine surfaces always carries an $\mathbb{A}^{1}$-fibration, possibly after a finite extension of the base. In the particular case where the general fibers of the…

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

We construct a smooth rational affine surface S with finite automorphism group but with the property that the group of automorphisms of the cylinder SxA^2 acts infinitely transitively on the complement of a closed subset of codimension at…

Let $\Lambda_0$ be an ordered abelian group. We show how an $\mathrm{ATF}(\mathbb{Z}\times\Lambda_0)$ group -- that is, a group admitting a free affine action without inversions on a $\mathbb{Z}\times\Lambda_0$-tree -- admits a natural…

We prove a factorization theorem for Fuchsian groups similar to those proved by Agol and Liu for 3-manifold groups. As an application, we build Makanin-Razborov diagrams, which parametrize the collection of all discrete representations from…

The affine Weyl group acts on the cohomology (with compact support) of affine Springer fibers (local Springer theory) and of parabolic Hitchin fibers (global Springer theory). In this paper, we show that in both situations, the action of…

Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids

In this paper we give a description of hypersurfaces with trivial ring $AK(S)$, introduced by the second author as following. Let $X$ be an affine variety and let $G(X)$ be the group generated by all $\Bbb {C}^+$-actions on $X$. Then…

We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to…

Presenting a finite group by a free product of finite cyclic groups the Hopf formula for the Schur multiplier affords also a covering group, and this has minimal exponent provided that the order of the generators is preserved. This…

We describe a simple criterion for showing that a group has Serre's property FA. By exhibiting a certain pattern of finite subgroups, we show that this criterion is satisfied by Aut(F_n) and SL(n,Z) when n>=3.

For a complex surface of general type with a relatively minimal genus 2 fibration, the bounds of the orders of the automorphism group of the fibration, of its abelian subgroups and of its cyclic subgroups are determined as linear functions…

We study unions of fundamental domains of a Fuchsian group, especially those with hyperbolic plane metric realizing the metric of the corresponding hyperbolic surface. We call these unions the \textit{geodesic covers} of the Fuchsian group…

We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the…

We study unirationality of actions of finite groups on Fano threefolds.

We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view,…

We will show the uniqueness of outer coactions of finite groups on the AFD factor of type II$_1$ along the arguments by Connes, Jones and Ocneanu. Namely, we construct the infinite tensor product type action, adopt it as the model action,…

We study the polynomial fibration induced by the equation of the Klein surfaces obtained as quotient of finite linear groups of automorphisms of the plane; this surfaces are of type A, D, E, corresponding to their singularities. The generic…

A pseudomodular group is a finite coarea nonarithmetic Fuchsian group whose cusp set is exactly $\mathbb{P}^1(\mathbb{Q})$. Long and Reid constructed finitely many of these by considering Fricke groups, i.e., those that uniformize…