Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A46

Retrieve articles in all journals with MSC: 30A46

Additional Information

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

American Mathematical Society