Non-flat extension of flat vector bundles

Indranil Biswas , Viktoria Heu (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We construct a pair (E ,F), where E is a holomorphic vector bundle over a compact Riemann surface and F a holomorphic subbundle of E, such that both F and E/F admit holomorphic connections, but E does not.

Domaines: Variables complexes [math.CV]

Indranil Biswas, Viktoria Heu. Non-flat extension of flat vector bundles. International Journal of Mathematics, 2015, 26 (14), pp.1550114. ⟨10.1142/S0129167X15501141⟩. ⟨hal-01062899⟩