We give a criterion for filtered vector bundles over curves to admit a filtration preserving meromorphic connection that induces a given meromorphic connection on the corresponding graded bundle.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Atiyah M F, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957) 181–207
Biswas I, A criterion for flatness of sections of adjoint bundle of a holomorphic principal bundle over a Riemann surface, Documenta Math. (to appear)
Biswas I and Heu V, Holomorphic connections on filtered bundles over curves, preprint
Biswas I and Heu V, Holomorphic connections on filtered bundles with given connection on the graded bundle, preprint
Esnault H and Viehweg E, Semistable bundles on curves and irreducible representations of the fundamental group. Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), 129–138, Contemp. Math., 241, Amer. Math. Soc., Providence, RI 1999
Weil A, Généralisation des fonctions abéliennes, Jour. Math. Pure Appl. 17 (1938) 47–87
The authors would like to thank Carlo Gasbarri for many inspiring discussions on this topic.
About this article
Cite this article
BISWAS, I., HEU, V. Meromorphic connections on vector bundles over curves. Proc Math Sci 124, 487–496 (2014). https://doi.org/10.1007/s12044-014-0201-8
- Meromorphic connection
- filtered bundle
- Atiyah bundle
2000 Mathematics Subject Classification