Algebraic surfaces of general type withK 2=2p g−1,p g≥5

Abstract

This paper mainly deals with minimal algebraic surfaces of general type withK 2=2p g−1. We prove that forp g≥7 all these surfaces are birational to a double cover of some rational surfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study their structures by determining their branch loci and singular fibres. We study similarly for surfaces withp g=5, 6. Lastly we show that whenp g≥13 all these surfaces are simply-connected.