EUDML

We give explicit constructions of all the numerical Campedelli surfaces, i.e. the minimal surfaces of general type with $K^{2} = 2$ and $p_{g} = 0$ , whose fundamental group has order 9. There are three families, one with $π_{1}^{alg} = ℤ_{9}$ and two with $π_{1}^{alg} = ℤ_{3}^{2}$ . We also determine the base locus of the bicanonical system of these surfaces. It turns out that for the surfaces with $π_{1}^{alg} = ℤ_{9}$ and for one of the families of surfaces with $π_{1}^{alg} = ℤ_{3}^{2}$ the base locus consists of two points. To our knowlegde, these are the only known examples of surfaces of general...

Brill–Noether loci for divisors on irregular varieties

Margarida Mendes Lopes; Rita Pardini; Pietro Pirola — 2014

Journal of the European Mathematical Society

We take up the study of the Brill-Noether loci $W^{r} (L, X) : = {η \in {Pic}^{0} (X) | h^{0} (L \otimes η) \geq r + 1}$ , where $X$ is a smooth projective variety of dimension $> 1$ , $L \in Pic (X)$ , and $r \geq 0$ is an integer. By studying the infinitesimal structure of these loci and the Petri map (defined in analogy with the case of curves), we obtain lower bounds for $h^{0} (K_{D})$ , where $D$ is a divisor that moves linearly on a smooth projective variety $X$ of maximal Albanese dimension. In this way we sharpen the results of [Xi] and we generalize them to dimension $> 2$ . In the $2$ -dimensional case we prove an...

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Some remarks on plane curves over fields of finite characteristic

Abelian covers of algebraic varieties.

Canonical images of surfaces.

On the period map for abelian covers of projective varieties

Prym varieties and the canonical map of surfaces of general type

A new family of surfaces with $p_{g} = 0$ and $K^{2} = 3$

Numerical Campedelli surfaces with fundamental group of order 9

Brill–Noether loci for divisors on irregular varieties