On the logarithmic connections over curves

Indranil Biswas (1) , Viktoria Heu (2)

1 Algebraic geometry
2 IRMA - Institut de Recherche Mathématique Avancée

We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves. Firstly, we establish a dictionary between logarithmic orbifold connections and parabolic logarithmic connections over the quotient curve. Secondly, we prove that fixed points on the moduli space of connections under the action of finite order line bundles are exactly the push-forward of logarithmic connections on a certain unramified Galois cover of the base curve. In the coprime case, this action of finite order line bundles on the moduli space is cohomologically trivial.

Mots clés: Logarithmic connection; residue; moduli space; Higgs bundle

Domaines: Géométrie algébrique [math.AG]

Indranil Biswas, Viktoria Heu. On the logarithmic connections over curves. Journal of the Ramanujan Mathematical Society, 2013, 28A (SPL). ⟨hal-00696247⟩