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

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 $\varphi_*\colon M^0(X)\to M^0(Y)$. 
@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/}
}
TY  - JOUR
AU  - I. V. Artamkin
TI  - Stable bundles with $c_1=0$ on rational surfaces
JO  - Izvestiya. Mathematics 
PY  - 1991
SP  - 231
EP  - 246
VL  - 36
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a0/
LA  - en
ID  - IM2_1991_36_2_a0
ER  - 
%0 Journal Article
%A I. V. Artamkin
%T Stable bundles with $c_1=0$ on rational surfaces
%J Izvestiya. Mathematics 
%D 1991
%P 231-246
%V 36
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1991_36_2_a0/
%G en
%F IM2_1991_36_2_a0
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/

[1] Barth W., “Moduli of vector bandies on the projective plane”, Invent. Math., 42 (1977), 63–91 | DOI | MR | Zbl

[2] Barth W., Hulek K., “Monads and moduli of vector bundles”, Manuscripta Math., 25 (1978), 323–347 | DOI | MR | Zbl

[3] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, UMN, 33:2 (1978), 85–134 | MR | Zbl

[4] Maruyama M., “Moduli of stable sheaves, I”, J. Math. Kyoto Univ., 17 (1977), 91–126 | MR | Zbl

[5] Maruyama M., “Openness of a family of torsion – free sheaves”, J. Math. Kyoto Univ., 16 (1976), 627–637 | MR | Zbl

[6] Okonek C., Schneider H., Spindler H., Vector bundles on complex projective spaces, Birkhauser, 1980 | MR

[7] Hulek K., “On the classification of stable rank-$r$ vector bundles over the projective planed”, Vector Bundles and Differential Equations (Proceedings of the Nice Conference, 1979), Progress in Mathematics, 7, Birkhäuser, Boston, Mass., 1980, 113–144 | MR

[8] Schwarzenberger R. L. E., “Vector bundles on algebraic surfaces, III”, Proc. London Math. Soc., 11:44 (1961), 601–622 | DOI | MR | Zbl

[9] Khodzh V., Pido D., Metody algebraicheskoi geometrii, II, IL, M., 1954