Related papers: On an Enriques surface associated with a quartic H…

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences…

Extending Enriques' characterization to algebraically closed fields of characteristic $p \geq 7$, we show that every smooth projective surface $X$ with $h^1(X, \mathcal{O}_X) = 2$ and $p_1(X) = p_2(X) = 1$ is birational to an Abelian…

We classify all possible automorphism groups of smooth cubic surfaces over an algebraically closed field of arbitrary characteristic. As an intermediate step we also classify automorphism groups of quartic del Pezzo surfaces. We show that…

We study the homeomorphism types of certain covers of (always orientable) surfaces, usually of infinite-type. We show that every surface with non-abelian fundamental group is covered by every noncompact surface, we identify the universal…

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 use semi-orthogonal decompositions to construct autoequivalences of Hilbert schemes of points on Enriques surfaces and of Calabi-Yau varieties which cover them. While doing this, we show that the derived category of a surface whose…

We describe the outer automorphism group of a one-ended fundamental group of a graph of groups, when edge groups are cyclic, and vertex groups are torsion-free with cyclic centralizers. We show that in this case the outer automorphism group…

We recall some properties, unfortunately not all, of the Cremona group. We first begin by presenting a nice proof of the amalgamated product structure of the well-known subgroup of the Cremona group made up of the polynomial automorphisms…

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…

This article gives the proof of results announced in [J. Blanc, Finite Abelian subgroups of the Cremona group of the plane, C.R. Acad. Sci. Paris, S\'er. I 344 (2007), 21-26.] and some description of automorphisms of rational surfaces.…

An abelian surface A over a field K has potential quaternionic multiplication if the ring End_\bar K (A) of geometric endomorphisms of A is an order in an indefinite rational division quaternion algebra. In this brief note, we study the…

We show that smooth hypersurfaces in complex projective spaces with automorphism groups of maximum size are isomorphic to Fermat hypersurfaces, with a few exceptions. For the exceptions, we give explicitly the defining equations and…

This paper develops families of complex Enriques surfaces whose Brauer groups pull back identically to zero on the covering K3 surfaces. Our methods rely on isogenies with Kummer surfaces of product type. We offer both lattice theoretic and…

We give a differentially closed description of the uniformizing representation to the analytical apparatus on Riemann surfaces and orbifolds of finite analytic type. Apart from well-known automorphic functions and Abelian differentials it…

We study the existence of linear series on curves lying on an Enriques surface and general in their complete linear system. Using a method that works also below the Bogomolov-Reider range, we compute, in all cases, the gonality of such…

We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group…

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of…

Graphs embedded into surfaces have many important applications, in particular, in combinatorics, geometry, and physics. For example, ribbon graphs and their counting is of great interest in string theory and quantum field theory (QFT).…

Let $X$ be a K3 or Enriques surface with good reduction. Let $G$ be a finite group acting (not necessarily linearly) on $X$. We give a criterion for this group action to extend to a smooth model of $X$ in terms of the action of $G$ on the…

Let $S$ be a compact Riemann surface and $G$ a group of conformal automorphisms of $S$ with $S_0 = S/G$. $S$ is a finite regular branched cover of $S_0$. If $U$ denotes the unit disc, let $\Gamma$ and $\Gamma_0$ be the Fuchsian groups with…