Geodesic
Logarithmic transformation of an elliptic surface, and vector bundles
Izvestiya. Mathematics, Tome 38 (1992) no. 3, pp. 455-469 
S. Zube. Logarithmic transformation of an elliptic surface, and vector bundles. Izvestiya. Mathematics, Tome 38 (1992) no. 3, pp. 455-469. http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a1/
@article{IM2_1992_38_3_a1,
     author = {S. Zube},
     title = {Logarithmic transformation of an elliptic surface, and vector bundles},
     journal = {Izvestiya. Mathematics},
     pages = {455--469},
     year = {1992},
     volume = {38},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a1/}
}
TY  - JOUR
AU  - S. Zube
TI  - Logarithmic transformation of an elliptic surface, and vector bundles
JO  - Izvestiya. Mathematics
PY  - 1992
SP  - 455
EP  - 469
VL  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a1/
LA  - en
ID  - IM2_1992_38_3_a1
ER  - 
%0 Journal Article
%A S. Zube
%T Logarithmic transformation of an elliptic surface, and vector bundles
%J Izvestiya. Mathematics
%D 1992
%P 455-469
%V 38
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a1/
%G en
%F IM2_1992_38_3_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

The author constructs mappings between bundles on an elliptic surface and bundles on an elliptic surface that has been modified by a logarithmic transformation. These mappings are applied to the study of the moduli varieties of bundles with $c_1=0$ on elliptic surfaces.

[1] Atiyah M. F., “Vector bundles over an elliptic curve”, Proc. Lond. Math. Soc., 27:3 (1957), 414–452 | DOI | MR

[2] Atiyah M. F., “Complex analitic conections in fibre bundles”, Trans. Amer. Math. Soc., 85 (1957), 181–207 | DOI | MR | Zbl

[3] Atiyah M. F., Bott R., “The Yang–Mills equations over Riemann surfaces”, Philos. Trans. Roy. Soc. London, 308 (1982), 523–615 | DOI | MR

[4] Bart W., Peters C., Van de Ven A., Compact complex surfaces, Springer, Berlin, Heidelberg, New York, 1984 | MR

[5] Friedman R., “Rank two vector bundles over regular elliptic surfaces”, Invent. math., 96:2 (1989), 283–333 | DOI | MR

[6] Kodaira K., “On the structure of complex analitic surfaces. I”, American J. of math., 86 (1967), 751–823 | DOI | MR