Geodesic
Stability of Vector Bundles on Curves and Degenerations
Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 858-864

Voir la notice de l'article provenant de la source Cambridge University Press

We introduce a weaker notion of (semi)stability for vector bundles on reducible curves that does not depend on a choice of polarization and suffices for many applications of degeneration techniques. We explore the basic properties of this alternate notion of (semi)stability. In a complementary direction, we record a proof of the existence of semistable extensions of vector bundles in suitable degenerations.
DOI : 10.4153/CMB-2016-008-2
Mots-clés : 14D06, 14H60, vector bundle, stability, degeneration 
Osserman, Brian. Stability of Vector Bundles on Curves and Degenerations. Canadian mathematical bulletin, Tome 59 (2016) no. 4, pp. 858-864. doi: 10.4153/CMB-2016-008-2
@article{10_4153_CMB_2016_008_2,
     author = {Osserman, Brian},
     title = {Stability of {Vector} {Bundles} on {Curves} and {Degenerations}},
     journal = {Canadian mathematical bulletin},
     pages = {858--864},
     year = {2016},
     volume = {59},
     number = {4},
     doi = {10.4153/CMB-2016-008-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-008-2/}
}
TY  - JOUR
AU  - Osserman, Brian
TI  - Stability of Vector Bundles on Curves and Degenerations
JO  - Canadian mathematical bulletin
PY  - 2016
SP  - 858
EP  - 864
VL  - 59
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-008-2/
DO  - 10.4153/CMB-2016-008-2
ID  - 10_4153_CMB_2016_008_2
ER  - 
%0 Journal Article
%A Osserman, Brian
%T Stability of Vector Bundles on Curves and Degenerations
%J Canadian mathematical bulletin
%D 2016
%P 858-864
%V 59
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-008-2/
%R 10.4153/CMB-2016-008-2
%F 10_4153_CMB_2016_008_2

[HL97] [HL97] Huybrechts, D. and Lehn, M., The geometry of moduli spaces of sheaves. Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschwieg, 1997. Google Scholar

[OT] [OT] Osserman, B. and Teixidor i Bigas, M., Linked symplectic forms and limit linear series in rank 2 with special determinant. Adv. Math. 288(2016), 576–630. http://dx.doi.Org/10.1016/j.aim.2015.09.030 Google Scholar

[Tei95] [Tei95] Teixidor i Bigas, M., Moduli spaces of vector bundles on reducible curves. Amer. J. Math. 117(1995), no. 1, 125–139. http://dx.doi.Org/10.2307/2375038 Google Scholar

[TeiO4] [TeiO4] Teixidor i Bigas, M., Rank two vector bundles with canonical determinant. Math. Nachr. 265(2004), 100–106. http://dx.doi.Org/10.1OO2/mana.2OO310138 Google Scholar

[TeiO8] [TeiO8] Teixidor i Bigas, M., Petri map for rank two bundles with canonical determinant. Compos. Math. 144(2008), no. 3, 705–720. http://dx.doi.Org/10.1112/S0010437X07003442 Google Scholar

[Zha] [Zha] Zhang, N., Towards the Bertram-Feinberg-Mukai conjecture. To appear, J. Pure and Appl. Algebra, http://dx.doi.Org/!0.1016/j.jpaa.2O15.09.020 Google Scholar

Cité par Sources :