Related papers: The degree of the bicanonical map of a surface wit…

A minimal surface of general type with $p_g(S)=0$ satisfies $1\le K^2\le 9$ and it is known that the image of the bicanonical map $\fie$ is a surface for $K_S^2\geq 2$, whilst for $K^2_S\geq 5$, the bicanonical map is always a morphism. In…

Let $S$ be a minimal surface of general type with $p_g = q = 1, K_S^2 = 7$. We prove that the degree of the bicanonical map is 1 or 2. Furthermore, if the degree is 2, we describe $S$ by a double cover.

Let $S$ be a minimal surface of general type with $p_g=0$ and $K^2=6$, such that its bicanonical map $\fie\colon S\to\pp^6$ is not birational. The map $\fie$ is a morphism of degree $\le 4$ onto a surface. The case of $\deg\fie=4$ is…

Let $S$ be a minimal surface of general type with $p_g(S) = 0, K_S^2 = 5$ and bicanonical map of degree 4. Denote by $\Sigma$ the bicanonical image. If $\Sigma$ is smooth, then $S$ is a Burniat surface; and if $\Sigma$ is singular, then we…

We study the minimal complex surfaces of general type with $p_g=0$ and $K^2=7$ or 8 whose bicanonical map is not birational. In the paper 'The bicanonical map of surfaces with $p_g=0$ and $K^2\ge 7$' we have shown that if $S$ is such a…

We give an up-to-date overview of the known results on the bicanonical map of surfaces of general type with $p_g=0$ and $K^2\ge 2$.

Let S be a minimal surface of general type with $p_g(S)=0$ and such that the bicanonical map $\phi:S\to \pp^{K^2_S}$ is a morphism: then the degree of $\phi$ is at most 4 and if it is equal to 4 then $K^2_S\le 6$. Here we prove that if…

Let S be a minimal complex surface of general type with p_g=0 such that the bicanonical map of S is not birational and let Z be the bicanonical image. In [M.Mendes Lopes, R.Pardini, "Enriques surfaces with eight nodes", Math. Zeit. 241 (4)…

We prove that if the bicanonical map of a minimal surface of general type S with p_{g}=q=1 and K^2=8 is non birational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification of…

This note describes minimal surfaces $S$ of general type satisfying $p_g\geq 5$ and $K^2=2p_g$. For $p_g\geq 8$ the canonical map of such surfaces is generically finite of degree 2 and the bulk of the paper is a complete characterization of…

Let $S$ be a minimal surface of general type with $p_{g}(S)=0$ and $K^{2}_{S}=4$. Assume the bicanonical map $\varphi$ of $S$ is a morphism of degree $4$ such that the image of $\varphi$ is smooth. Then we prove that the surface $S$ is a…

It is shown that the canonical ring of a minimal surface of general type with $p_g=0, K^2\geq 2$ is generated by its elements of degree lesser or equal to 5, provided $|2K|$ has no fixed components, and that this bound can be lowered to 4…

We give a list of possibilities for surfaces of general type with $p_g=0$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$ and $S/i$ is not rational. Some examples with $K^2=4,...,7$ are constructed as…

We study surfaces of general type $S$ with $p_g=0$ and $K^2=3$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$. It is shown that, if $S/i$ is not rational, then $S/i$ is birational to an Enriques…

We construct a surface of general type with canonical map of degree 12 which factors as a triple cover and a bidouble cover of $\mathbb P^2$. We also show the existence of a smooth surface with $q=0,$ $\chi=13$ and $K^2=9\chi$ such that its…

Let X be a minimal complex surface of general type such that its image via the canonical map is a surface; we denote by d the degree of the canonical map. In this expository work, first of all we recall the known possibilities for the…

We consider $(1,1)$-surfaces, namely, minimal compact complex surfaces $S$ with $p_g (S) =K_S^2=1$: for these the bicanonical map is a covering of degree $4$ of the plane $\mathbb{P}^2$. And we answer a question posed by Meng Chen, whether…

We prove that the bicanonical map of a surfaces of general S type with p_g=q=0 is non birational if there exists a pencil on S whose general member is an hyperelliptic curve of genus 3.

We consider a family of surfaces of general type $S$ with $K_S$ ample, having $K^2_S = 24, p_g (S) = 6, q(S)=0$. We prove that for these surfaces the canonical system is base point free and yields an embedding $\Phi_1 : S \rightarrow…

We study minimal complex surfaces S of general type with q(S)=q and p_g(S)=2q-3, q>= 5. We give a complete classification in case that S has a fibration onto a curve of genus >=2. For these surfaces K^2=8\chi. In general we prove that…