On surfaces with pg = q = 1 and non-ruled bicanonical involution

Abstract

This paper classifies surfaces of general type S with pg = q = 1 having an involution i such that S/i has non-negative Kodaira dimension and that the bicanonical map of S factors through the double cover induced by i. It is shown that S/i is regular and either: a) the Albanese fibration of S is of genus 2 or b) S has no genus 2 fibration and S/i is birational to a K3 surface. For case a) a list of possibilities and examples are given. An example for case b) with K 2 = 6 is also constructed. 2000 Mathematics Classification: 14J29.