Related papers: A brief introduction to Enriques surfaces

We present some (unfortunately not all) known properties on the Cremona group; when it's possible we mentioned links with the most known group of polynomial automorphisms of the affine plane. The mentioned properties are essentially…

We describe a period map for those simply connected Enriques surfaces in characteristic 2 whose canonical double cover is K3. The moduli stack for these surfaces has a Deligne-Mumford quotient that is an open substack of a $\mathbb…

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.

Let $X$ be an Enriques surface. Using Beauville's result about the triviality of the Brauer map of $X$, we define a new involution on the category of coherent sheaves on the canonically covering K3 surface $\overline{X}$. We relate the…

We point out an interesting relation between hypersurface elliptic singularities and log Enriques surfaces: with a few exceptions, every hypersurface elliptic singularity define some klt log Enriques surface $(S,Diff)$. In many cases, the…

In this paper we determine automorphism groups of cyclic algebraic curves defined over finite fields of any characteristic.

These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.

There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.

We prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.

We give obstructions - in terms of Gaussian maps - for a marked Prym curve $(C,\alpha,T_d)$ to admit a singular model lying on an Enriques surface with only one $d$-ordinary point singularity and in such a way that $T_d$ corresponds to the…

In this survey we discuss the problem of the existence of rational curves on complex surfaces, both in the K\"ahler and non-K\"ahler setup. We systematically go through the Enriques--Kodaira classification of complex surfaces to highlight…

We complete our study of linear series on curves lying on an Enriques surface by showing that, with the exception of smooth plane quintics, there are no exceptional curves on Enriques surfaces, that is, curves for which the Clifford index…

The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…

Combinatorial aspects of the Torelli-Johnson-Morita theory of surface automorphisms are extended to certain subgroups of the mapping class groups. These subgroups are defined relative to a specified homomorphism from the fundamental group…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

We characterize simple complex abelian varieties and simple abelian surfaces in terms of primitivity of translation automorphisms. Applying this together with a result due to Diller and Favre, we then classify all primitive birational…

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…

Recent results on initial segments of the Turing degrees are presented, and some conjectures about initial segments that have implications for the existence of non-trivial automorphisms of the Turing degrees are indicated.

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…