Surfaces of general type with K2=2χ−1

Abstract

We classify minimal algebraic surfaces of general type having K2=2χ−1 and χ≥7. Such surfaces are regular with canonical map of degree one or two. If pg≥13, then the surface is a genus-two fibration; otherwise we use the canonical map to describe these surfaces as birational either to the canonical image or to a double cover of a rational surface.