Journal of the Ramanujan Mathematical Society

Volume 28A, Issue SPL, July – Special Issue 2013 pp. 21–40.

On the logarithmic connections over curves

Authors: Indranil Biswas and Viktoria Heu
Author institution: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

Summary: We study two different actions on the moduli spaces of logarithmic connections over smooth complex projective curves; one given by the automorphisms of the base curve and the other given by the torsion points of suitable order of the Jacobian of the curve. 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.

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