The bicanonical map of surfaces with $p_g=0$ and $K^2\ge 7$, II
| dc.creator | Lopes, Margarida Mendes | |
| dc.creator | Pardini, Rita | |
| dc.date | 2001-11-13 | |
| dc.date.accessioned | 2026-07-07T04:44:35Z | |
| dc.date.available | 2026-07-07T04:44:35Z | |
| dc.description | 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 surface, then the bicanonical map has degree 2. Here we describe precisely such surfaces showing that there is a fibration $f\colon S\to \pp^1$ such that: i) the general fibre $F$ of $f$ is a genus 3 hyperelliptic curve; ii) the involution induced by the bicanonical map of $S$ restricts to the hyperelliptic involution of $F$. Furthermore, if $K^2_S=8$, then $f$ is an isotrivial fibration with 6 double fibres, and if $K^2_S=7$, then $f$ has 5 double fibres and it has precisely one fibre with reducible support, consisting of two components. | |
| dc.description | Latex 2e, 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0111160 | |
| dc.identifier | http://arxiv.org/abs/math/0111160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62645 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The bicanonical map of surfaces with $p_g=0$ and $K^2\ge 7$, II | |
| dc.type | text |