Comptes Rendus
no. 2
Algebraic geometry
A note on 1-cycles on the moduli space of rank-2 bundles over a curve
[Une note sur les 1-cycles des espaces de module des fibrés vectoriels de rang 2 sur une courbe]

Présenté par : Claire Voisin

Duo Li1 ; Yinbang Lin1 ; Xuanyu Pan2
1 Yau Mathematical Sciences Center, Tsinghua University, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 209-211.

Nous étudions les 1-cycles des espaces de module de fibrés vectoriels de rang 2 et déterminant de degré 1 fixé, sur une courbe complexe, projective, lisse, de genre ≥3. Nous montrons que le groupe de Chow d'indice 1 des espaces de module est isomorphe au groupe de Chow d'indice 0 de la courbe.

Over a smooth complex projective curve of genus ≥3, we study 1-cycles on the moduli space of rank-2 stable vector bundles with fixed determinant of degree 1. We show the first Chow group of the moduli space is isomorphic to the zeroth Chow group of the curve.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.12.003
Duo Li 1 ; Yinbang Lin 1 ; Xuanyu Pan 2

1 Yau Mathematical Sciences Center, Tsinghua University, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China 
@article{CRMATH_2019__357_2_209_0,
     author = {Duo Li and Yinbang Lin and Xuanyu Pan},
     title = {A note on 1-cycles on the moduli space of rank-2 bundles over a curve},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {209--211},
     publisher = {Elsevier},
     volume = {357},
     number = {2},
     year = {2019},
     doi = {10.1016/j.crma.2018.12.003},
     language = {en},
}
TY  - JOUR
AU  - Duo Li
AU  - Yinbang Lin
AU  - Xuanyu Pan
TI  - A note on 1-cycles on the moduli space of rank-2 bundles over a curve
JO  - Comptes Rendus. Mathématique
PY  - 2019
SP  - 209
EP  - 211
VL  - 357
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2018.12.003
LA  - en
ID  - CRMATH_2019__357_2_209_0
ER  - 
%0 Journal Article
%A Duo Li
%A Yinbang Lin
%A Xuanyu Pan
%T A note on 1-cycles on the moduli space of rank-2 bundles over a curve
%J Comptes Rendus. Mathématique
%D 2019
%P 209-211
%V 357
%N 2
%I Elsevier
%R 10.1016/j.crma.2018.12.003
%G en
%F CRMATH_2019__357_2_209_0
Duo Li; Yinbang Lin; Xuanyu Pan. A note on 1-cycles on the moduli space of rank-2 bundles over a curve. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 209-211. doi : 10.1016/j.crma.2018.12.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.12.003/

[1] M.F. Atiyah; R. Bott The Yang–Mills equations over Riemann surfaces, Philos. Trans. R. Soc. Lond. Ser. A, Volume 308 (1983) no. 1505, pp. 523-615

[2] I. Choe; J.-M. Hwang Chow group of 1-cycles on the moduli space of vector bundles of rank 2 over a curve, Math. Z., Volume 253 (2006) no. 2, pp. 281-293

[3] S. Del Baño On the motive of moduli spaces of rank two vector bundles over a curve, Compos. Math., Volume 131 (2002) no. 1, pp. 1-30

[4] J.-M. Drezet; M.S. Narasimhan Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques, Invent. Math., Volume 97 (1989) no. 1, pp. 53-94

[5] S. Kilaru Rational curves on moduli spaces of vector bundles, Proc. Indian Acad. Sci. Math. Sci., Volume 108 (1998) no. 3, pp. 217-226

[6] A. King; A. Schofield Rationality of moduli of vector bundles on curves, Indag. Math. (N.S.), Volume 10 (1999) no. 4, pp. 519-535

[7] S. Ramanan The moduli spaces of vector bundles over an algebraic curve, Math. Ann., Volume 200 (1973), pp. 69-84

[8] Z. Tian; H.R. Zong One-cycles on rationally connected varieties, Compos. Math., Volume 150 (2014) no. 3, pp. 396-408

[9] C. Voisin Stable birational invariants and the Lüroth problem, Surveys in Differential Geometry 2016. Advances in Geometry and Mathematical Physics, Surv. Differ. Geom., vol. 21, Int. Press, Somerville, MA, USA, 2016, pp. 313-342

Cité par Sources :

Commentaires - Politique