Geodesic
Stable bundles with $c_1=0$ on rational surfaces
Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 231-246

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For an arbitrary rational surface $X$the author proves the existence of a nonempty component of the moduli variety $M^0(X,n,r)$ of rank $r$ bundles with $c_1=0$ and $c_2=n\geqslant r$ in which the $\mathscr L$-stable bundles constitute a nonempty open subset for any ample $\mathscr L$. Moreover, any birational isomorphism $\varphi\colon X\to Y$ of surfaces gives rise to a birational isomorphism $\varphi_*\colon M^0(X)\to M^0(Y)$. 
@article{IM2_1991_36_2_a0,
     author = {I. V. Artamkin},
     title = {Stable bundles with $c_1=0$ on rational surfaces},
     journal = {Izvestiya. Mathematics },
     pages = {231--246},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {1991},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a0/}
}
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I. V. Artamkin. Stable bundles with $c_1=0$ on rational surfaces. Izvestiya. Mathematics , Tome 36 (1991) no. 2, pp. 231-246. http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a0/