Related papers: Complex projective surfaces and infinite groups

We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively…

We study linear systems of surfaces in $\mathbb{P}^3$ singular along general lines. Our purpose is to identify and classify special systems of such surfaces, i.e., those nonempty systems where the conditions imposed by the multiple lines…

We construct a surface of general type with invariants \( \chi = K^2 = 1 \) and torsion group \( \Bbb{Z}/{2} \). We use a double plane construction by finding a plane curve with certain singularities, resolving these, and taking the double…

This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…

For the base field of complex numbers we discuss the relationship between categories of coherent sheaves on compact Riemann surfaces and categories of coherent sheaves on weighted smooth projective curves. This is done by bringing back to…

The general {\bf surface group conjecture} asks whether a one-relator group where every subgroup of finite index is again one-relator and every subgroup of infinite index is free (property IF) is a surface group. We resolve several related…

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

We consider translation surfaces with poles on surfaces. We shall prove that any finite group appears as the automorphism group of some translation surface with poles. As a direct consequence we obtain the existence of structures achieving…

We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular,…

Using quantum representations of mapping class groups we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic…

We introduce the special and general projectivity groups attached to a simplex $F$ of a thick irreducible spherical building of simply laced type. If the residue of $F$ is irreducible, we determine the permutation group of both projectivity…

In this paper, we prove the Shafarevich conjecture for proper hyperbolic polycurves, which is a higher dimensional analogue of that for proper hyperbolic curves. First, we study theories of proper hyperbolic polycurves over regular schemes.…

We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the…

Real Legendrian subvarieties are classical objects of differential geometry and classical mechanics and they have been studied since antiquity. However, complex Legendrian subvarieties are much more rigid and have more exceptional…

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.

Surfaces of amplitude 1 in ordinary projective space are of general type, but this need not be the case in weighted projective spaces. Indeed, there are 4 classes of quasi-smooth weighted hypersurfaces in $\mathbf{P}(1,2,a,b)$ of amplitude…

Let $X$ be a smooth projective variety defined over an algebraically closed field, and let $L$ be an ample line bundle over $X$. We prove that for any smooth hypersurface $D$ on $X$ in the complete linear system $| L^{\otimes d}|$, the…

It is shown that various questions about the existence of simple closed curves in normal subgroups of surface groups are undecidable.

Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…

We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that for every finitely-presented group G there is a complex projective surface S with simple normal…