Related papers: Surfaces close to the Severi lines

If an irreducible curve on the very general Enriques surface splits in the K3 cover, its preimage consists of two linearly equivalent irreducible curves. We prove the nonemptiness of countable families of Severi varieties of curves of any…

We construct a surface with log terminal singularities and ample canonical class that has $K_X^2=1/48 983$ and a log canonical pair $(X,B)$ with a nonempty reduced divisor $B$ and ample $K_X+B$ that has $(K_X+B)^2 = 1/462$. Both examples…

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…

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we…

We shall study minimal complex surfaces with $c^2 = 9$ and $\chi=5$ whose canonical classes are divisible by $3$ in the integral cohomology groups, where $c_1^2$ and $\chi$ denote the first Chern number of an algebraic surface and the Euler…

Let S be a smooth algebraic surface satisfying the following property: H^i(\oc_S(C))=0 (i=1,2) for any irreducible and reduced curve C of S. The aim of this paper is to provide a characterization of special linear systems on S which are…

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $20$, and that if equality is attained, then the…

Let $S$ be a minimal irregular surface of general type, whose Albanese map induces a hyperelliptic fibration $f:\,S \to B$ of genus $g$.We prove a quadratic upper bound on the genus $g$, i.e., $g\leq h\big(\chi(\mathcal{O}_S)\big)$, where…

We settle the first step for the classification of surfaces of general type with K^2 = 8, p_g = 4 and q = 0, classifying the even surfaces (K is 2-divisible). The first even surfaces of general type with $K^2=8$, $p_g=4$ and $q=0$ were…

In this paper, we classify the minimal surfaces of general type with $\chi=5$, $K^{2}=9$ whose canonical map is composed with an involution. We obtain 6 families, whose dimensions in the moduli space are 28, 27, 33, 32, 31 and 32…

We classify all the irrational pencils over the surfaces of general type with p=q=2. This classification adds a new evidence to a Catanese conjecture which states that if S has p=q=2 but no irrational pencils then it is the double cover of…

Let $S$ be a minimal surface of general type with irregularity $q(S) = 1$. Well-known inequalities between characteristic numbers imply that $3 p_g(S) \le c_2(S) \le 10 p_g(S)$, where $p_g(S)$ is the geometric genus and $c_2(S)$ the…

We complement recent work of Gallardo, Pearlstein, Schaffler, and Zhang, showing that the stable surfaces with $K_X^2 =1$ and $\chi(\mathcal O_X) = 3$ they construct are indeed the only ones arising from imposing an exceptional unimodal…

The blow-up of the anticanonical base point on a del Pezzo surface $S$ of degree 1 gives rise to a rational elliptic surface $\mathscr{E}$ with only irreducible fibers. The sections of minimal height of $\mathscr{E}$ are in correspondence…

In this paper, we study algebraic surfaces of general type with $p_g=q=1$ and genus 2 Albanese fibrations. We first study the examples of surfaces with $p_g=q=1, K^2=5$ and genus 2 Albanese fibrations constructed by Catanese using singular…

We show that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 12, if the minimal resolution of $X$ is not a…

Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over…

Let $\mathcal X\to\mathbb D$ be a flat family of projective complex 3-folds over a disc $\mathbb D$ with smooth total space $\mathcal X$ and smooth general fibre $\mathcal X_t,$ and whose special fiber $\mathcal X_0$ has double normal…

Let $S$ be a rational surface with $\dim|-K_S|\ge 1$ and let $\pi: X\rightarrow S$ be a ramified cyclic covering from a nonruled smooth surface $X$. We show that for any integer $k\ge 3$ and ample divisor $A$ on $S$, the adjoint divisor…

We study Severi curves parametrizing rational bisections of elliptic fibrations associated to general pencils of plane cubics. Our main results show that these Severi curves are connected and reduced, and we give an upper bound on their…