Surfaces of general type with K2=2χ−1

Abstract

We classify minimal algebraic surfaces of general type having $K^2=2\chi -1$ and $\chi \ge 7$. Such surfaces are regular with canonical map of degree one or two. If $p_g\ge 13$, 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.