Related papers: Veech groups of flat surfaces with poles

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

We survey recent developments on mapping class groups of surfaces of infinite topological type.

We prove that every orientable infinite type surface without boundary and finite genus has a Riemann surface structure such that its modular group of quasiconformal homeomorphisms is countable.

Let X be a closed oriented Riemann surface of genus > 1 of constant negative curvature -1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus > 3…

We compute the algebraic $K$-theory of some classes of surfaces defined over finite fields. We achieve this by first calculating the motivic cohomology groups and then studying the motivic Atiyah-Hirzebruch spectral sequence. In an…

Let $A$ be an abelian surface over a finite field $k$. The $k$-isogeny class of $A$ is uniquely determined by a Weil polynomial $f_A$ of degree 4. We give a classification of the groups of $k$-rational points on varieties from this class in…

We study the Euler class of smooth orientable infinite-type surface bundles with a section. For many such surfaces, we show that this cohomology class is nontrivial, and that the behavior of its powers depends on the genus and the type of…

Beauville surfaces are a class of complex surfaces defined by letting a finite group $G$ act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the…

Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for…

We give a classification of generic coadjoint orbits for the groups of symplectomorphisms and Hamiltonian diffeomorphisms of a closed symplectic surface. We also classify simple Morse functions on symplectic surfaces with respect to actions…

We prove that a ``bouillabaisse'' surface (translation surface which has two transverse parabolic elements) has totally real trace field. As a corollary, non trivial Veech groups which have no parabolic elements do exist. The proof follows…

Let $\AAutH (X)$ be the subgroup of the group $\AutH (X)$ of holomorphic automorphisms of a normal affine algebraic surface $X$ generated by elements of flows associated with complete algebraic vector fields. Our main result is a…

A group action is said to be highly-transitive if it is $k$-transitive for every $k \ge 1$. The main result of this thesis is the following: Main Theorem: The fundamental group of a closed, orientable surface of genus > 1 admits a…

A smooth algebraic surface $S$ is said to be \emph{isogenous to a product of unmixed type} if there exist two smooth curves $C, F$ and a finite group $G$, acting faithfully on both $C$ and $F$ and freely on their product, so that $S=(C…

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.

We give a description of asymptotic quadratic growth rates for geodesic segments on covers of Veech surfaces in terms of the modular fiber parameterizing coverings of a fixed Veech surface. To make the paper self contained we derive the…

Atiyah classifies vector bundles on elliptic curves $E$ over an algebraically closed field of any characteristic. On the other hand, a rank $2$ vector bundle on $E$ defines a surface $S$ with a $\mathbb{P}^1$-bundle structure on $E$. We…

This paper describes the geometry and topology of leaves of the isoperiodic foliation of the stratum $\Omega\mathcal{M}_1(1,1,-2)$. We prove that each leaf is a surface of infinite genus homeomorphic to the Loch Ness monster surface and…

We construct examples of flat surfaces in $\mathbb{H}^3$ which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in $\mathbb{H}^3$ with only one end and at most two isolated singularities.

This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichm\"uller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for…