Branched structures and affine and projective bundles on Riemann surfaces

Mandelbaum, Richard

doi:10.1090/S0002-9947-1973-0325958-9

Branched structures and affine and projective bundles on Riemann surfaces
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Trans. Amer. Math. Soc. 183 (1973), 37-58 Request permission

Abstract:

A classification for analytic branched G-structures on a Riemann surface M is provided by means of a map ${\phi _G}$, into the moduli spaces of flat G-bundles on $M.\;(G = {\text {GA}}(1,{\text {C}})$ or ${\text {PL}}(1,{\text {C}}).)$ Conditions are determined under which ${\phi _G}$ is injective and these conditions are related to the total branching order of the G-structures. A decomposition of the space of analytic branched G-structures into a disjoint union of analytic varieties is exhibited and it is shown that ${\phi _G}$ is is fact holomorphic on each such variety.

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