A holomorphic chain on a compact Riemann surface is a tuple of vector bundles together with homomorphisms between them. We show that the moduli space of holomorphic chains of rank one is identified with a fiber product of projective space bundles. We compute the Euler characteristic of the moduli space. The stability of chains involves real vector parameters. We also show that the variation of parameters corresponds to the characters of Gm.
On the moduli space of holomorphic G-connections on a compact Riemann surface
Line bundles on the moduli space of parabolic connections over a compact Riemann surface
A note on the moduli spaces of holomorphic and logarithmic connections over a compact Riemann surface
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