Comptes Rendus
Research article - Algebraic geometry
Moduli of rank 2 vector bundles over a curve
Xucheng Zhang1  
1 Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1915-1918

We show that among rank 2 vector bundles over a curve only semistable and simple objects admit a good moduli space.

Nous montrons que parmi les fibrés vectoriels de rang 2 sur une courbe, seuls les objets semistables et simples admettent de bons espaces de modules.

Received:
Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/crmath.628
Classification: 14D20, 14D23
Keywords: Vector bundles, Moduli space, Algebraic stacks
Mots-clés : Fibrés vectoriels, Espaces de modules, Champs algébriques

Xucheng Zhang 1

1 Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
@article{CRMATH_2024__362_G13_1915_0,
     author = {Xucheng Zhang},
     title = {Moduli of rank 2 vector bundles over a curve},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1915--1918},
     year = {2024},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     doi = {10.5802/crmath.628},
     zbl = {07962939},
     language = {en},
}
TY  - JOUR
AU  - Xucheng Zhang
TI  - Moduli of rank 2 vector bundles over a curve
JO  - Comptes Rendus. Mathématique
PY  - 2024
SP  - 1915
EP  - 1918
VL  - 362
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.628
LA  - en
ID  - CRMATH_2024__362_G13_1915_0
ER  - 
%0 Journal Article
%A Xucheng Zhang
%T Moduli of rank 2 vector bundles over a curve
%J Comptes Rendus. Mathématique
%D 2024
%P 1915-1918
%V 362
%I Académie des sciences, Paris
%R 10.5802/crmath.628
%G en
%F CRMATH_2024__362_G13_1915_0
Xucheng Zhang. Moduli of rank 2 vector bundles over a curve. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1915-1918. doi: 10.5802/crmath.628

[1] Jarod Alper; Daniel Halpern-Leistner; Jochen Heinloth Existence of moduli spaces for algebraic stacks, Invent. Math., Volume 234 (2023) no. 3, pp. 949-1038 | DOI | MR | Zbl

[2] Michael F. Atiyah Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., Volume 85 (1957), pp. 181-207 | DOI | MR | Zbl

[3] Dario Weissmann; Xucheng Zhang A stacky approach to identify the semistable locus of bundles (2023) (https://arxiv.org/abs/2302.09245)

Cited by Sources:

Comments - Policy