Related papers: Automorphisms of smooth fine curve graphs

We show that a continuous map $f$ from a quasi-graph $G$ to itself is pointwise recurrent if and only if one of the following two statements holds: (1) $X$ is a simple closed curve and $f$ is topologically conjugate to an irrational…

We prove autoduality for curves of compact type and, more generally, treelike curves with planar singularities. More precisely, we produce an isomorphism between the generalized Jacobian of such a curve and the connected component of the…

Let $X/S$ be a smooth family of smooth projective varieties, where $S$ is a smooth affine curve over a field $k$ of characteristic $0.$ We relate the differential fundamental groupoid scheme of $X/k$ with the differential fundamental…

We give necessary and sufficient topological conditions for a simple closed curve on a real rational surface to be approximable by smooth rational curves. We also study approximation by smooth rational curves with given complex…

We prove that for a homeomorphism f that is isotopic to the identity on a closed hyperbolic surface, the following are equivalent: * f acts hyperbolically on the fine curve graph; * f is isotopic to a pseudo-Anosov map relative to a finite…

A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U^g=V. Here, extending work of Lachlan on finite homogeneous digraphs, we classify finite…

We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…

In this paper, we consider the problem of determining which automorphisms of a smooth quartic surface $S \subset \mathbb{P}^3$ are induced by a Cremona transformation of $\mathbb{P}^3$. We provide the first steps towards a complete solution…

We consider systems of simple closed curves on surfaces and their total number of intersection points, their so-called crossing number. For a fixed number of curves, we aim to minimise the crossing number. We determine the minimal crossing…

The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…

We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or equi-generic…

Complex Enriques surfaces with a finite group of automorphisms are classified into seven types. In this paper, we determine which types of such Enriques surfaces exist in characteristic 2. In particular we give a one dimensional family of…

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 prove that each injective simplicial map from the arc complex of a compact, connected, nonorientable surface with nonempty boundary to itself is induced by a homeomorphism of the surface. We also prove that the automorphism group of the…

The group of 2-by-2 matrices with integer entries and determinant $\pm > 1$ can be identified either with the group of outer automorphisms of a rank two free group or with the group of isotopy classes of homeomorphisms of a 2-dimensional…

We show that every auto-homeomorphism of the unmeasured lamination space of an orientable surface of finite type is induced by a unique extended mapping class unless the surface is a sphere with at most four punctures or a torus with at…

To every half-translation surface, we associate a saddle connection graph, which is a subgraph of the arc graph. We prove that every isomorphism between two saddle connection graphs is induced by an affine homeomorphism between the…

A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their…

Let $S$ be a regular minimal surface of general type over the field of complex numbers, and $\mathrm{Aut}_\mathbb{Q}(S)$ the subgroup of automorphisms acting trivially on $H^*(S,\mathbb{Q})$. It has been known since twenty years that…

In this paper we classify non-symplectic automorphisms of order 8 on complex K3 surfaces in case that the fourth power of the automorphism has only rational curves in its fixed locus. We show that the fixed locus is the disjoint union of a…