On the classification of surfaces of general type with non-birational bicanonical map and Du Val Double planes

TL;DR

This paper classifies certain complex algebraic surfaces of general type with specific bicanonical map properties, focusing on those with a degree 2 map onto rational or ruled surfaces.

Contribution

It provides a classification of surfaces of general type with non-birational bicanonical maps, specifically those composed with a degree 2 rational map.

Findings

Classification of surfaces with non-birational bicanonical maps

Identification of cases where the bicanonical map factors through a degree 2 rational map

Insights into the structure of Du Val Double planes

Abstract

We classify surfaces of general type whose bicanonical map is composed with a rational map of degree 2 onto a rational or ruled surface.