On the Classification of Surfaces of General Type with Non-birational Bicanonical Map and Du Val Double Planes

@inproceedings{Borrelli2008OnTC,
title={On the Classification of Surfaces of General Type with Non-birational Bicanonical Map and Du Val Double Planes},
author={Giuseppe Borrelli},
year={2008}
}

We classify surfaces of general type whose bicanonical map φ2K is composed with a rational map of degree 2 onto a rational or ruled surface. In particular, this is always the case if q = 0, pg ≥ 2 and φ2K is not birational. We prove that such a surface S either has a genus 2 pencil or is the smooth model of a double plane branched along a reduced curve with certain singularities, a configuration already suggested by Du Val in the 1950’s. In the last case we show that S has a rational pencil |C… CONTINUE READING