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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Branched structures and affine and projective bundles on Riemann surfaces


Author: Richard Mandelbaum
Journal: Trans. Amer. Math. Soc. 183 (1973), 37-58
MSC: Primary 30A46
MathSciNet review: 0325958
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0325958-9
PII: S 0002-9947(1973)0325958-9
Keywords: Branched structures, Riemann surface, affine structure, projective structure, affine bundle, projective bundle, divisor, affine variety, analytic variety
Article copyright: © Copyright 1973 American Mathematical Society