On the stability of flat complex vector bundles over parallelizable manifolds
- Publication type:
- Journal article
- Metadata:
-
- Autoren
- Indranil Biswas
- Sorin Dumitrescu
- Manfred Lehn
- Autoren-URL
- https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000447284300005&DestLinkType=FullRecord&DestApp=WOS_CPL
- DOI
- 10.1016/j.crma.2018.08.001
- eISSN
- 1778-3569
- Externe Identifier
- Clarivate Analytics Document Solution ID: GW9EG
- ISSN
- 1631-073X
- Ausgabe der Veröffentlichung
- 10
- Zeitschrift
- COMPTES RENDUS MATHEMATIQUE
- Paginierung
- 1030 - 1035
- Datum der Veröffentlichung
- 2018
- Status
- Published
- Titel
- On the stability of flat complex vector bundles over parallelizable manifolds
- Sub types
- Article
- Ausgabe der Zeitschrift
- 356
Data source: Web of Science (Lite)
- Other metadata sources:
-
- Autoren
- Indranil Biswas
- Sorin Dumitrescu
- Manfred Lehn
- DOI
- 10.1016/j.crma.2018.08.001
- eISSN
- 1778-3569
- Ausgabe der Veröffentlichung
- 10
- Zeitschrift
- Comptes Rendus. Mathématique
- Sprache
- en
- Online publication date
- 2018
- Paginierung
- 1030 - 1035
- Status
- Published online
- Herausgeber
- Cellule MathDoc/Centre Mersenne
- Herausgeber URL
- http://dx.doi.org/10.1016/j.crma.2018.08.001
- Datum der Datenerfassung
- 2024
- Titel
- On the stability of flat complex vector bundles over parallelizable manifolds
- Ausgabe der Zeitschrift
- 356
Data source: Crossref
- Abstract
- We investigate the flat holomorphic vector bundles over compact complex parallelizable manifolds $G / \Gamma$, where $G$ is a complex connected Lie group and $\Gamma$ is a cocompact lattice in it. The main result proved here is a structure theorem for flat holomorphic vector bundles $E_\rho$ associated to any irreducible representation $\rho : \Gamma \rightarrow \text{GL}(r,{\mathbb C})$. More precisely, we prove that $E_{\rho}$ is holomorphically isomorphic to a vector bundle of the form $E^{\oplus n}$, where $E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in particular, its degree is zero. We deduce a stability result for flat holomorphic vector bundles $E_{\rho}$ of rank 2 over $G/ \Gamma$. If an irreducible representation $\rho : \Gamma\rightarrow \text{GL}(2, \mathbb {C})$ satisfies the conditionmthat the induced homomorphism $\Gamma\rightarrow {\rm PGL}(2, {\mathbb C})$ does not extend to a homomorphism from $G$, then $E_{\rho}$ is proved to be stable.
- Autoren
- Indranil Biswas
- Sorin Dumitrescu
- Manfred Lehn
- Autoren-URL
- http://arxiv.org/abs/1709.05951v2
- Schlüsselwörter
- math.DG
- math.DG
- math.AG
- 53B21, 53C56, 53A55
- Notes
- Comptes Rendus Math\'ematique (to appear)
- Datum der Veröffentlichung
- 2017
- Datum der Datenerfassung
- 2017
- Datum, an dem der Datensatz öffentlich gemacht wurde
- 2017
- Titel
- On the stability of flat complex vector bundles over parallelizable manifolds
Files
1709.05951v2.pdf
Data source: arXiv
- Autoren
- Indranil Biswas
- Sorin Dumitrescu
- Manfred Lehn
- DOI
- 10.1016/j.crma.2018.08.001
- ISSN
- 1631-073X
- Zeitschrift
- Comptes Rendus Mathématique. Académie des Sciences. Paris
- Notes
- mrclass: 32L05 (14J60 32M10 32Q26 53C30) mrnumber: 3864198 mrreviewer: J. T. Davidov
- Artikelnummer
- 10
- Paginierung
- 1030 - 1035
- Datum der Veröffentlichung
- 2018
- Herausgeber URL
- https://doi.org/10.1016/j.crma.2018.08.001
- Datum der Datenerfassung
- 2019
- Titel
- On the stability of flat complex vector bundles over parallelizable manifolds
- Sub types
- article
- Ausgabe der Zeitschrift
- 356
Data source: Manual
- Beziehungen:
- Property of