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

Li, Duo1 ; Lin, Yinbang1 ; Pan, Xuanyu2
1 Yau Mathematical Sciences Center, Tsinghua University, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
Comptes Rendus. Mathématique, Tome 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
Li, Duo 1 ; Lin, Yinbang 1 ; Pan, Xuanyu 2

1 Yau Mathematical Sciences Center, Tsinghua University, China
2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China 
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Li, Duo; Lin, Yinbang; Pan, Xuanyu. A note on 1-cycles on the moduli space of rank-2 bundles over a curve. Comptes Rendus. Mathématique, Tome 357 (2019) no. 2, pp. 209-211. doi : 10.1016/j.crma.2018.12.003. http://www.numdam.org/articles/10.1016/j.crma.2018.12.003/

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

[2] Choe, I.; Hwang, J.-M. 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] Del Baño, S. 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] Drezet, J.-M.; Narasimhan, M.S. 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] Kilaru, S. Rational curves on moduli spaces of vector bundles, Proc. Indian Acad. Sci. Math. Sci., Volume 108 (1998) no. 3, pp. 217-226

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

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

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

[9] Voisin, C. 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

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