相关论文: The bicanonical map of surfaces with $p_g=0$ and $…

In this paper we study on the involution on minimal surfaces of general type with $p_g=q=0$ and $K^2=7$. We focus on the classification of the birational models of the quotient surfaces and their branch divisors induced by an involution.

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…

We study minimal {\em double planes} of general type with $K^2=8$ and $p_g=0$, namely pairs $(S,\sigma)$, where $S$ is a minimal complex algebraic surface of general type with $K^2=8$ and $p_g=0$ and $\sigma$ is an automorphism of $S$ of…

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 prove that the bicanonical map of the Cartwright-Steger surface is an embedding. We also discuss two minimal surfaces of general type, both covered by the Cartwright-Steger surface. One has $K^2=2$, $p_g=1$, $\pi_1=\{1\}$ and the other…

We study the construction of complex minimal smooth surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. Inoue constructed the first examples of such surfaces, which can be described as Galois $\mathbb{Z}_2\times\mathbb{Z}_2$-covers…

We classify surfaces of general type whose bicanonical map is composed with a rational map of degree 2 onto a rational or ruled surface.

An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces…

We construct two complex-conjugated rigid surfaces with $p_g=q=2$ and $K^2=8$ whose universal cover is not biholomorphic to the bidisk. We show that these are the unique surfaces with these invariants and Albanese map of degree $2$, apart…

The aim of this article is to classify the pairs (S, G), where S is a smooth minimal surface of general type with p_g=0 and K^2=7, G is a subgroup of the automorphism group of S and G is isomorphic to the group $\mathbb{Z}_2^2$. The Inoue…

In this paper we classify completely all regular minimal surfaces with K^2=8, p_g=4 whose canonical map is composed with an involution. We obtain six unirational families of respective dimensions 28,28,32,33,38,34. The last two are…

Let $f:S \fr B$ be a surface fibration with fibres of genus 5. We find a linear relation between the fundamental invariants of the surface. Namely $K_f^2=\chi_f+N$ where $N$ is the number of trigonal fibres. Our proof is based on the…

Given a relatively minimal fibration $f: S \to \Bbb P^1$ on a rational surface $S$ with general fiber $C$ of genus $g$, we investigate under what conditions the inequality $6(g-1)\le K_f^2$ occurs, where $K_f$ is the canonical relative…

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…

In this article we study the bicanonical map $\phi_2$ of quadruple Galois canonical covers X of surfaces of minimal degree. We show that $\phi_2$ has diverse behavior and exhibit most of the complexities that are possible for a bicanonical…

A nodal Enriques surface can have at most 8 nodes. We give an explicit description of Enriques surfaces with 8 nodes, showing that they are quotients of products of elliptic curves by a group isomorphic to $\Z_2^2$ or to $\Z_2^3$ acting…

By a theorem of Reider, a twisted bicanonical system, that means a linear system of divisors numerically equivalent to a bicanonical divisor, on a minimal surface of general type, is base point free if $K^2_S \geq 5$. Twisted bicanonical…

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 consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every…

We study minimal surfaces X of general type with $K^2_X=6p_g-14$ and $q(X)>0$ such that $K_X$ is ample, the image of the canonical map is a canonically embedded surface of general type and the canonical map is not birational. The main…