[Simplicité des fibrés tangents des espaces de modules des fibrés symplectiques et orthogonaux sur une courbe]
La variété des tangentes des courbes minimales rationnelles associés aux courbes de Hecke, a été utilisée par J.-M. Hwang [8] pour prouver la simplicité du fibré tangent à l’espace de modules des fibrés vectoriels sur une courbe. Nous utilisons les applications tangentes des courbes de Hecke symplectiques et orthogonales pour démontrer un résultat analogue pour les fibrés symplectiques et orthogonaux. En particulier, nous prouvons que la variété des tangentes aux courbes rationnelles minimales associée est non dégénérée ; ce qui implique la simplicité des fibrés tangents aux espaces de modules des fibrés symplectiques et orthogonaux sur une courbe. Nous montrons d’ailleurs, pour genre suffisamment grand, que l’application tangente est un plongement pour un fibré symplectique ou orthogonal générique.
The variety of minimal rational tangents associated to Hecke curves was used by J.-M. Hwang [8] to prove the simplicity of the tangent bundle on the moduli of vector bundles over a curve. In this paper, we use the tangent maps of the symplectic and orthogonal Hecke curves to prove an analogous result for symplectic and orthogonal bundles. In particular, we show the nondegeneracy of the associated variety of minimal rational tangents, which implies the simplicity of the tangent bundle on the moduli spaces of symplectic and orthogonal bundles over a curve. We also show that for large enough genus, the tangent map is an embedding for a general symplectic or orthogonal bundle.
Révisé le :
Accepté le :
Publié le :
Mots clés : symplectic bundle, orthogonal bundle, minimal rational tangents
Insong Choe 1 ; George H. Hitching 2 ; Jaehyun Hong 3
CC-BY 4.0
@article{CRMATH_2024__362_G5_493_0,
author = {Insong Choe and George H. Hitching and Jaehyun Hong},
title = {Simplicity of {Tangent} bundles on the moduli spaces of symplectic and orthogonal bundles over a curve},
journal = {Comptes Rendus. Math\'ematique},
pages = {493--510},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
year = {2024},
doi = {10.5802/crmath.560},
language = {en},
}
TY - JOUR AU - Insong Choe AU - George H. Hitching AU - Jaehyun Hong TI - Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve JO - Comptes Rendus. Mathématique PY - 2024 SP - 493 EP - 510 VL - 362 PB - Académie des sciences, Paris DO - 10.5802/crmath.560 LA - en ID - CRMATH_2024__362_G5_493_0 ER -
%0 Journal Article %A Insong Choe %A George H. Hitching %A Jaehyun Hong %T Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve %J Comptes Rendus. Mathématique %D 2024 %P 493-510 %V 362 %I Académie des sciences, Paris %R 10.5802/crmath.560 %G en %F CRMATH_2024__362_G5_493_0
Insong Choe; George H. Hitching; Jaehyun Hong. Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 493-510. doi : 10.5802/crmath.560. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.560/
[1] Brill–Noether loci on moduli spaces of symplectic bundles over curves, Collect. Math., Volume 72 (2021) no. 2, pp. 443-469 | DOI | MR | Zbl
[2] Isotropic Quot schemes of orthogonal bundles over a curve, Int. J. Math., Volume 32 (2021) no. 8, 2150047 | DOI | MR | Zbl
[3] Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles, J. Lond. Math. Soc., Volume 105 (2022) no. 1, pp. 543-564 | DOI | MR | Zbl
[4] Maximal isotropic subbundles of orthogonal bundles of odd rank over a curve, Int. J. Math., Volume 26 (2015) no. 13, 1550106 | DOI | MR | Zbl
[5] Low rank orthogonal bundles and quadric fibrations, J. Korean Math. Soc., Volume 60 (2023) no. 6, pp. 1137-1169 | DOI | MR | Zbl
[6] Subbundles of symplectic and orthogonal vector bundles over curves, Math. Nachr., Volume 280 (2007) no. 13-14, pp. 1510-1517 | DOI | MR | Zbl
[7] Hecke curves and Hitchin discriminant, Ann. Sci. Éc. Norm. Supér., Volume 37 (2004) no. 5, pp. 801-817 | DOI | Numdam | MR | Zbl
[8] Tangent vectors to Hecke curves on the moduli space of rank 2 bundles over an algebraic curve, Duke Math. J., Volume 101 (2000) no. 1, pp. 179-187 | DOI | MR | Zbl
[9] Hecke curves on the moduli space of vector bundles over an algebraic curve, Algebraic geometry in East Asia (Kyoto, 2001), World Scientific, 2002, pp. 155-164 | DOI | MR | Zbl
[10] Zur Klassifikation von Regelmannigfaltigkeiten, Math. Ann., Volume 262 (1983) no. 4, pp. 447-459 | DOI | MR | Zbl
[11] Deformations of the moduli space of vector bundles over an algebraic curve, Ann. Math., Volume 101 (1975), pp. 391-417 | DOI | MR | Zbl
[12] Geometry of Hecke cycles. I, C. P. Ramanujam – A tribute (Tata Institute of Fundamental Research Studies in Mathematics), Volume 8, Springer, 1978, pp. 291-345 | MR | Zbl
[13] Minimal rational curves on moduli spaces of stable bundles, Math. Ann., Volume 331 (2005) no. 4, pp. 925-937 | DOI | MR | Zbl
Cité par Sources :
Commentaires - Politique