Related papers: Hypermaps and multiply quasiplatonic Riemann surfa…

Motivated by the theory of Riemann surfaces, we classify all possibilities for finite simple groups acting faithfully on a compact Riemann surface of genus at least 2 in such a way that all non-trivial elements have at most three fixed…

Let X be a closed surface of genus two embedded in the 3-sphere. Then X inherits a metric and an orientation, which give an almost complex structure, which automatically integrates to a genuine complex structure, making X a Riemann surface.…

We introduce the Plaque Topology on the inverse limit of a branched covering self-map of a Riemann surface of a finite degree greater than one. We present the notions of regular and irregular points in the setting of this Plaque Inverse…

We look for Riemann surfaces whose automorphism group acts transitively on the Weierstrass points. We concentrate on hyperelliptic surfaces, surfaces with PSL(2, q) as automorphism group, Platonic surfaces and Fermat curves.

We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this…

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…

We introduce a simple procedure to integrate differential forms with arbitrary holomorphic poles on Riemann surfaces. It gives rise to an intrinsic regularization of such singular integrals in terms of the underlying conformal geometry.…

We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams…

We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…

We prove the existence of a one parameter family of minimal embedded hypersurfaces in $R^{n+1}$, for $n \geq 3$, which generalize the well known 2 dimensional "Riemann minimal surfaces". The hypersurfaces we obtain are complete, embedded,…

We classify compact Riemann surfaces of genus $g$, where $g-1$ is a prime $p$, which have a group of automorphisms of order $\rho(g-1)$ for some integer $\rho\ge 1$, and determine isogeny decompositions of the corresponding Jacobian…

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on…

We develope basic geometric quantities and properties of hypersurfaces in Carnot groups.

Let $m \geqslant 6$ be an even integer. In this short note we prove that the Jacobian variety of a quasiplatonic Riemann surface with associated group of automorphisms isomorphic to $C_2^2 \rtimes_2 C_m$ admits complex multiplication. We…

We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via…

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…

A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…

The complement of a Cantor set in the complex plane is itself regarded as a Riemann surface of infinite type. The problem is the quasiconformal equivalence of such Riemann surfaces. Particularly, we are interested in Riemann surfaces given…

In this short note, we prove the existence of infinitely many pairwise non-isomorphic non-hyperelliptic Riemann surfaces with automorphism group acting transitively on the Weierstrass points. We also found all those compact Riemann 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…