A construction of stable bundles on an algebraic surface (Q1104992)

Let X be a smooth projective complex surface of geometric genus \(p_ g\) and let H be an ample divisor on X. The main result is the following: ``If \(n\geq 4([p_ g/2]+1)\), then there is an H-stable bundle E on X of rank two having \(c_ 1(E)=0\) and \(c_ 2(E)=n\); moreover, if \(p_ g>1000\) the same conclusion holds for \(n>(3/2)p_ g+6''\). This sharpens the result of \textit{C. H. Taubes} [J. Differ. Geom. 19, 517-560 (1984; Zbl 0552.53011)], which asserts the existence of such bundles whenever \(n\geq (8/3)p_ g+2\).