Geodesic
Stable bundles with $c_1=0$ on rational surfaces
Izvestiya. Mathematics, Tome 36 (1991) no. 2, pp. 231-246 
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/
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     author = {I. V. Artamkin},
     title = {Stable bundles with $c_1=0$ on rational surfaces},
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     volume = {36},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\varphi_*\colon M^0(X)\to M^0(Y)$.

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