Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve
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 resul...
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.560/ |
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| author | Choe, Insong H. Hitching, George Hong, Jaehyun |
| author_facet | Choe, Insong H. Hitching, George Hong, Jaehyun |
| author_sort | Choe, Insong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dbdfd3aae3ad4069b39f7c2daa8b768b |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-dbdfd3aae3ad4069b39f7c2daa8b768b2025-02-07T11:21:12ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G549351010.5802/crmath.56010.5802/crmath.560Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curveChoe, Insong0H. Hitching, George1Hong, Jaehyun2Department of Mathematics, Konkuk University, 1 Hwayang-dong, Gwangjin-Gu, Seoul 143-701, Republic of KoreaOslo Metropolitan University, Postboks 4, St. Olavs plass, 0130 Oslo, NorwayCenter for Complex Geometry, Institute for Basic Science (IBS), Daejeon 34126, Republic of KoreaThe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.560/symplectic bundleorthogonal bundleminimal rational tangents |
| spellingShingle | Choe, Insong H. Hitching, George Hong, Jaehyun Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve Comptes Rendus. Mathématique symplectic bundle orthogonal bundle minimal rational tangents |
| title | Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| title_full | Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| title_fullStr | Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| title_full_unstemmed | Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| title_short | Simplicity of Tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| title_sort | simplicity of tangent bundles on the moduli spaces of symplectic and orthogonal bundles over a curve |
| topic | symplectic bundle orthogonal bundle minimal rational tangents |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.560/ |
| work_keys_str_mv | AT choeinsong simplicityoftangentbundlesonthemodulispacesofsymplecticandorthogonalbundlesoveracurve AT hhitchinggeorge simplicityoftangentbundlesonthemodulispacesofsymplecticandorthogonalbundlesoveracurve AT hongjaehyun simplicityoftangentbundlesonthemodulispacesofsymplecticandorthogonalbundlesoveracurve |