Chern slopes of simply connected complex surfaces of general type are dense in [2,3

Abstract

We prove that for any number r 2 [2;3], there are spin (resp. nonspin and minimal) simply connected complex surfaces of general type X with c 2(X)=c2(X) arbitrarily close to r. In particular, this shows the existence of simply connected surfaces of general type arbitrarily close to the Bogomolov-Miyaoka-Yau line. In addition, we prove that for any r2 [1;3] and any integer q 0, there are minimal complex surfaces of general type X with c 2(X)=c2(X) arbitrarily close to r and 1(X) isomorphic to the fundamental group of a compact Riemann surface of genus q.