Géométrie algébrique
Une Note sur les fibrés holomorphes non-filtrables
Comptes Rendus. Mathématique, Tome 336 (2003) no. 7, pp. 581-584.

On démontre que tout fibré vectoriel holomorphe de rang deux, non-filtrable, sur une surface elliptique non-kählérienne est une modification élémentaire d'une image directe d'un fibré en droites par un revêtement double de la surface.

We prove that any non-filtrable holomorphic rank-2 vector bundle on a non-Kähler elliptic surface is an elementary modification of a direct image of a line bundle by a double covering of the surface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00139-0
Aprodu, Marian 1, 2 ; Toma, Matei 2, 3

1 Université de Grenoble 1, institut Fourier, BP 74, 38402 Saint Martin d'Hères cedex, France
2 Romanian Academy, Institute of Mathematics “Simion Stoilow”, PO Box 1-764, 70700 Bucharest, Romania
3 Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069, Osnabrück, Germany
@article{CRMATH_2003__336_7_581_0,
     author = {Aprodu, Marian and Toma, Matei},
     title = {Une {Note} sur les fibr\'es holomorphes non-filtrables},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {581--584},
     publisher = {Elsevier},
     volume = {336},
     number = {7},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00139-0},
     language = {fr},
     url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00139-0/}
}
TY  - JOUR
AU  - Aprodu, Marian
AU  - Toma, Matei
TI  - Une Note sur les fibrés holomorphes non-filtrables
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 581
EP  - 584
VL  - 336
IS  - 7
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00139-0/
DO  - 10.1016/S1631-073X(03)00139-0
LA  - fr
ID  - CRMATH_2003__336_7_581_0
ER  - 
%0 Journal Article
%A Aprodu, Marian
%A Toma, Matei
%T Une Note sur les fibrés holomorphes non-filtrables
%J Comptes Rendus. Mathématique
%D 2003
%P 581-584
%V 336
%N 7
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00139-0/
%R 10.1016/S1631-073X(03)00139-0
%G fr
%F CRMATH_2003__336_7_581_0
Aprodu, Marian; Toma, Matei. Une Note sur les fibrés holomorphes non-filtrables. Comptes Rendus. Mathématique, Tome 336 (2003) no. 7, pp. 581-584. doi : 10.1016/S1631-073X(03)00139-0. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00139-0/

[1] Aprodu, M.; Brı̂nzănescu, V. On the holomorphic rank-2 vector bundles with trivial discriminant over non-Kähler elliptic bundles, J. Math. Kyoto Univ., Volume 42 (2002) no. 4

[2] Atiyah, M. Vector bundles over an elliptic curve, Proc. London Math. Soc., Volume 7 (1957), pp. 181-207

[3] Bănică, C.; Le Potier, J. Sur l'existence des fibrés vectoriels holomorphes sur les surfaces non-algébriques, J. Reine Angew. Math., Volume 378 (1987), pp. 1-31

[4] Brı̂nzănescu, V. Holomorphic Vector Bundle Over Compact Complex Surfaces, Lecture Notes in Math., 1624, Springer-Verlag, 1996

[5] Brı̂nzănescu, V.; Flondor, P. Holomorphic 2-vector bundles on non-algebraic 2-tori, J. Reine Angew. Math., Volume 363 (1985), pp. 47-58

[6] Brı̂nzănescu, V.; Ueno, K. Néron–Severi group for torus quasi bundles over curves, Moduli of Vector Bundles (Sanda, 1994; Kyoto, 1994), Lecture Notes in Pure and Appl. Math., 179, Dekker, New York, 1996, pp. 11-32

[7] Friedman, R. Rank two vector bundles over regular elliptic surfaces, Invent. Math., Volume 96 (1989), pp. 283-332

[8] Friedman, R. Algebraic Surfaces and Holomorphic Vector Bundles, Universitext, Springer-Verlag, 1998

[9] Fujiki, A. Countability of the Douady space of a complex space, Japan J. Math., Volume 5 (1979), pp. 431-447

[10] Fujiki, A. On the Douady space of a compact complex space in the category 𝒞. II, Publ. Res. Inst. Math. Sci., Volume 20 (1984), pp. 461-489

[11] Kodaira, K.; Kodaira, K.; Kodaira, K. On compact analytic surfaces. III, Ann. Math., Volume 71 (1960), pp. 111-152

[12] Teleman, A.; Toma, M. Holomorphic vector bundles on non-algebraic surfaces, C. R. Acad. Sci. Paris, Volume 334 (2002), pp. 1-6

[13] M. Toma, Holomorphic vector bundles on non-algebraic surfaces, Dissertation, Bayreuth, 1992

[14] Toma, M. Stable bundles with small c2 over 2-dimensional complex tori, Math. Z., Volume 232 (1999), pp. 511-525

[15] Toma, M. Compact moduli spaces of stable sheaves over non-algebraic surfaces, Documenta Math., Volume 6 (2001), pp. 9-27

[16] Vuletescu, V. Relating vector bundles on a nonalgebraic surface with those on its blow-up, An. Stiint. Univ. “Ovidius” Constanta Ser. Mat., Volume 5 (1997), pp. 111-114

Cité par Sources :