Algebraic Surfaces of General Type with K~2 = 2pg-1, pg■5

This paper mainly deals with minimal algebraic surfaces of general type with K~2=2p-1. We prove that for p7 all these surfaces are birational to a double cover of some rationalsurfaces, and all but a finite classes of them have a unique fibration of genus 2; then we study theirstructures by determining their branch loci and singular fibres. We study similarly for surfaces withp=5, 6. Lastly we show that when p13 all these surfaces are simply-connected.