The classification of double planes of general type with $K^2=8$ and $p_g=0$
| dc.creator | Pardini, Rita | |
| dc.date | 2001-07-13 | |
| dc.date.accessioned | 2026-07-07T04:42:35Z | |
| dc.date.available | 2026-07-07T04:42:35Z | |
| dc.description | We study minimal {\em double planes} of general type with $K^2=8$ and $p_g=0$, namely pairs $(S,σ)$, where $S$ is a minimal complex algebraic surface of general type with $K^2=8$ and $p_g=0$ and $σ$ is an automorphism of $S$ of order 2 such that the quotient $S/σ$ is a rational surface. We prove that $S$ is a free quotient $(F\times C)/G$, where $C$ is a curve, $F$ is an hyperelliptic curve, $G$ is a finite group that acts faithfully on $F$ and $C$, and $σ$ is induced by the automorphism $τ\times Id$ of $F\times C$, $τ$ being the hyperelliptic involution of $F$. We describe all the $F$, $C$ and $G$ that occur: in this way we obtain 5 families of surfaces with $p_g=0$ and $K^2=8$, of which we believe only one was previously known. Using our classification we are able to give an alternative description of these surfaces as double covers of the plane, thus recovering a construction proposed by Du Val. In addition we study the geometry of the subset of the moduli space of surfaces of general type with $p_g=0$ and $K^2=8$ that admit a double plane structure. | |
| dc.description | LaTeX2e, 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0107100 | |
| dc.identifier | http://arxiv.org/abs/math/0107100 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61847 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J29 | |
| dc.title | The classification of double planes of general type with $K^2=8$ and $p_g=0$ | |
| dc.type | text |