Related papers: On Coble surfaces and their automorphisms

In this work, we want to show several properties of an unnodal, complex Coble surface $X$ with irreducible boundary curve $C \in |-2 K_X|$. Namely, we show that every isotropic sequence ${\cal E}_1, \ldots, {\cal E}_r$ with $r \le 8$ and…

We classify Coble surfaces with finite automorphism group in arbitrary characteristic not equal to 2. There are exactly 9 isomorphism classes of such surfaces.

We study Coble surfaces in characteristic 2, in particular, singularities of their canonical coverings. As an application we classify Coble surfaces with finite automorphism group in characteristic 2. There are exactly 9 types of such…

A smooth rational surface X is a Coble surface if the anti-canonical linear system is empty while the anti-bicanonical linear system is non-empty. In this note we shall classify these X and consider the finiteness problem of the number of…

We construct some positive entropy automorphisms of rational surfaces with no periodic curves. The surfaces in question, which we term tri-Coble surfaces, are blow-ups of the projective plane at 12 points which have contractions down to…

We show that the Coble hypersurfaces, uniquely characterized by the remarkable property that their singular loci are an abelian surface and a Kummer threefold, respectively, belong to a family of hypersurfaces exhibiting similar behavior,…

We give conceptual proofs of some results on the automorphism group of an Enriques surface X, for which only computational proofs have been available. Namely, there is an obvious upper bound on the image of Aut(X) in the isometry group of…

Let A be an indecomposable principally polarized abelian variety of dimension g . Third order theta functions embed A in a projective space P(V_3), while second order theta functions embed the Kummer variety K=A/<-1> in a projective space…

In this paper, we prove that each automorphism of a surface braid group is induced by a homeomorphism of the underlying surface, provided that this surface is a closed, connected, orientable surface of genus at least 2, and the number of…

In this paper we give an explicit description of the automorphism group of a primary Kodaira surface $X$ in terms of suitable liftings to the universal cover $\mathbb{C}^2$. As it happens for complex tori, the automorphism group of $X$ is…

In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…

Following an idea of Ishida, we develop polynomial equations for certain unramified double covers of surfaces with p_g=q=1 and K^2=2. Our first main result provides an explicit surface surface X with these invariants defined over Q that has…

We study the family of irreducible curves with $\delta$ nodes belonging to a free linear system $|C|$ with smooth general member on a surface $S$ such that $|K_S|$ is ample. Under the assumption that $C$ is numerically equivalent to $pK_S$,…

We describe a family of smooth contractible algebraic surfaces $X$ different from $\C^2$ such that $X$ admits dominant holomorphic maps from $\C^2$ and there is a unique line $E$ in $X$ for which the Kobayashi-Royden pseudometric vanishes…

Let S be a connected, compact and orientable surface of genus two having exactly one boundary component. We study automorphisms of the Torelli complex for S, and describe any isomorphism between finite index subgroups of the Torelli group…

We investigate space curves with large cohomology. To this end we introduce curves of subextremal type. This class includes all subextremal curves. Based on geometric and numerical characterizations of curves of subextremal type, we show…

We say a smooth projective surface $X$ satisfies the bounded cohomology property if there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. Let the closed Mori…

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…

It follows from an observation of A. Coble in 1919 that the automorphism group of an unnodal Enriques surface contains the $2$-congruence subgroup of the Weyl group of the $E_{10}$-lattice. In this article, we determine how much bigger the…

Let $X$ be a complex projective surface with arbitrary singularities. We construct a generalized Abel--Jacobi map $A_0(X)\to J^2(X)$ and show that it is an isomorphism on torsion subgroups. Here $A_0(X)$ is the appropriate Chow group of…