Surfaces with p_g=q=1, K^2=8 and nonbirtional bicanonical map

TL;DR

This paper classifies minimal surfaces of general type with specific invariants, showing that nonbirational bicanonical maps imply the surface is a double cover of a rational surface.

Contribution

It proves that such surfaces with nonbirational bicanonical maps are double covers of rational surfaces, providing a complete classification for these cases.

Findings

Nonbirational bicanonical map implies double cover of rational surface.

Complete classification of surfaces with p_g=q=1, K^2=8, and nonbirational bicanonical map.

Surfaces with these invariants are characterized as double covers of rational surfaces.

Abstract

We prove that if the bicanonical map of a minimal surface of general type S with p_{g}=q=1 and K^2=8 is non birational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification of minimal surfaces of general type with p_{g}=q=1, K^2=8 and nonbirational bicanonical map.