Related papers: Affine surfaces and their Veech groups

We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the…

We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…

We study complements of hypersurfaces in schemes with respect to the property being affine.

We provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite.

We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems…

We study the action of the formal affine Hecke algebra on the formal group algebra, and show that the the formal affine Hecke algebra has a basis indexed by the Weyl group as a module over the formal group algebra. We also define a concept…

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

We propose and develop a theory that allows to characterize epimorphisms of profinite groups in terms of indecomposable epimorphisms.

We introduce the notion of a "graded topological space": a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of…

We propose a construction of affine space (or "polynomial rings") over a triangulated category, in the context of stable derivators.

Classes of branched surfaces extend the classes of surfaces or 2-dimensional manifolds satisfying suitable properties and defined in various manners. Reeb spaces of smooth maps of suitable classes into surfaces whose codimensions are…

We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…

The aim of this paper is to give a local description of affine surfaces, whose induced Blaschke structure is projectively flat. We show that such affine surfaces with constant Gauss affine curvature and indefinite induced Blaschke metric…

We study a global theory of affine maximal surfaces with singularities, which are called affine maximal maps and defined by Aledo--Mart\' inez--Mil\' an. In this paper, we define a special subclass of such surfaces other than improper…

$p$-Adic compactifications of geometric loop and diffeomorphism groups of compact manifolds on finite-dimensional spaces over non-Archimedean fields are investigated. Weakened topology is introduced. The structure of newly constructed…

In this paper we study the general affine differential geometry of surfaces in affine space $A^3$. For a regular elliptical surface we define a moving frame of minimal order and get the complete system of differential invariants. As an…

This article is a revised version of the talk I gave at the conference ``Beauville Surfaces and groups'' held in Newcastle in June 2012. It presents some group theoretical methods to give bounds on the number of connected components of the…

This is a brief overview of a few selected chapters on automorphism groups of affine varieties. It includes some open questions.

The paper contains a general construction which produces new examples of non simply-connected smooth projective surfaces. We analyze the resulting surfaces and their fundamental groups. Many of these fundamental groups are expected to be…

In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.