no. 2
Uniform Steiner bundles
[Fibrés de Steiner uniformes]
Marchesi, Simone1 ; Miró-Roig, Rosa Maria1
1 Universitat de Barcelona Facultat de Matemàtiques i Informàtica Gran Via de les Corts Catalanes 585 08007 Barcelona (Spain)
Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 447-472.

Dans ce travail, nous étudions les fibrés uniformes de Steiner de type k, ou k est le degré le plus bas de la décomposition. Nous prouvons des limites supérieures et inférieures strictes pour le rang dans le cas k=1 et, de plus, nous donnons des familles d’exemples pour chaque rang possible et nous expliquons quelle relation existe entre les familles. Après avoir traité le cas k en général, nous conjecturons que chaque fibré uniforme de Steiner de type k est obtenu par la technique de construction proposée.

In this work we study k-type uniform Steiner bundles, being k the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case k=1 and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case k in general, we conjecture that every k-type uniform Steiner bundle is obtained through the proposed construction technique.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3403
Classification : 14F05, 14J60
Keywords: Uniform bundles, Steiner bundles
Mot clés : Fibrés de Steiner, Fibrés uniformes
Marchesi, Simone 1 ; Miró-Roig, Rosa Maria 1

1 Universitat de Barcelona Facultat de Matemàtiques i Informàtica Gran Via de les Corts Catalanes 585 08007 Barcelona (Spain)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{AIF_2021__71_2_447_0,
     author = {Marchesi, Simone and Mir\'o-Roig, Rosa Maria},
     title = {Uniform {Steiner} bundles},
     journal = {Annales de l'Institut Fourier},
     pages = {447--472},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {71},
     number = {2},
     year = {2021},
     doi = {10.5802/aif.3403},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3403/}
}
TY  - JOUR
AU  - Marchesi, Simone
AU  - Miró-Roig, Rosa Maria
TI  - Uniform Steiner bundles
JO  - Annales de l'Institut Fourier
PY  - 2021
SP  - 447
EP  - 472
VL  - 71
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.3403/
DO  - 10.5802/aif.3403
LA  - en
ID  - AIF_2021__71_2_447_0
ER  - 
%0 Journal Article
%A Marchesi, Simone
%A Miró-Roig, Rosa Maria
%T Uniform Steiner bundles
%J Annales de l'Institut Fourier
%D 2021
%P 447-472
%V 71
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.3403/
%R 10.5802/aif.3403
%G en
%F AIF_2021__71_2_447_0
Marchesi, Simone; Miró-Roig, Rosa Maria. Uniform Steiner bundles. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 447-472. doi : 10.5802/aif.3403. https://aif.centre-mersenne.org/articles/10.5802/aif.3403/

[1] Arrondo, Enrique; Marchesi, Simone Jumping pairs of Steiner bundles, Forum Math., Volume 27 (2015), pp. 3233-3267 | MR | Zbl

[2] Ballico, Edoardo Uniform vector bundles of rank n+1 on ℙ n , Tsukuba J. Math., Volume 7 (1983), pp. 215-226 | MR | Zbl

[3] Ballico, Edoardo; Malaspina, Francesco Weakly uniform rank two vector bundles on multiprojective spaces, Bull. Aust. Math. Soc., Volume 84 (2011) no. 2, pp. 255-260 | DOI | MR | Zbl

[4] Ballico, Edoardo; Newstead, Peter E. Uniform bundles on quadric surfaces and some related varieties, J. Lond. Math. Soc., Volume 31 (1985) no. 2, pp. 211-223 | DOI | MR | Zbl

[5] Besana, GianMario; Fania, Maria L.; Flamini, Flaminio On families of rank-2 uniform bundles on Hirzebruch surfaces and Hilbert schemes of their scrolls, Rend. Ist. Mat. Univ. Trieste, Volume 47 (2015), pp. 27-44 | MR | Zbl

[6] Dolgachev, Igor; Kapranov, Mikhail Arrangements of hyperplanes and vector bundles on ℙ n , Duke Math. J., Volume 71 (1993) no. 3, pp. 633-664 | MR

[7] Drézet, Jean-Marc Exemples des fibrés uniformes non homogènes sur ℙ n , C. R. Math. Acad. Sci. Paris, Volume 291 (1980), pp. 125-128 | MR | Zbl

[8] Elencwajg, Georges Les fibrés uniformes de rang 3 sur ℙ 2 (C) sont homogènes, Math. Ann., Volume 231 (1978) no. 3, pp. 217-227 | DOI | Zbl

[9] Elencwajg, Georges Des fibrés uniformes non homogènes, Math. Ann., Volume 239 (1979) no. 2, pp. 185-192 | DOI | MR | Zbl

[10] Elencwajg, Georges; Hirschowitz, André; Schneider, Michael Les fibrés uniformes de rang au plus n sur ℙ n (ℂ) sont ceux qu’on croit, Vector bundles and differential equations (Nice, 1979) (Progress in Mathematics), Volume 7 (1980), pp. 37-63 | DOI | Zbl

[11] Ellia, Philippe Sur les fibrés uniformes de rang (n+1) sur ℙ n , Mém. Soc. Math. Fr., Nouv. Sér., Volume 7 (1982), pp. 1-60 | Zbl

[12] Ellia, Philippe; Menegatti, Paolo Spaces of matrices of constant rank and uniform vector bundles, Linear Algebra Appl., Volume 507 (2016), pp. 474-485 | DOI | MR | Zbl

[13] Muñoz, Roberto; Occhetta, Gianluca; Conde, Luis E. Solá Uniform vector bundles on Fano manifolds and applications, J. Reine Angew. Math., Volume 664 (2012), pp. 141-162 | MR | Zbl

[14] Okonek, Christian; Schneider, Michael; Spindler, Heinz Vector bundles on complex projective spaces, Progress in Mathematics, 3, Birkhäuser, 1980

[15] Sato, Eichi Uniform vector bundles on a projective space, J. Math. Soc. Japan, Volume 28 (1976), pp. 123-132 | MR

[16] Schwarzenberger, Rolph L. E. Vector bundles on the projective plane, Proc. Lond. Math. Soc., Volume 11 (1961), pp. 623-640 | DOI | MR | Zbl

[17] van de Ven, Antonius On uniform vector bundles, Math. Ann., Volume 195 (1972), pp. 245-248 | DOI | MR | Zbl

[18] Wiśniewski, Jaroslav Uniform vector bundles on Fano manifolds and an algebraic proof of Hwang–Mok characterization of Grassmannians, Complex geometry (Göttingen, 2000), Springer, 2002, pp. 329-340 | DOI | Zbl

[19] Xin, He Remarks on uniform bundles on projective spaces, Ann. Univ. Ferrara, Sez. VII, Sci. Mat., Volume 64 (2018) no. 2, pp. 449-463 | DOI | MR | Zbl

Cité par Sources :