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Complex Manifolds

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Equivariant principal bundles for G–actions and G–connections

Indranil Biswas
  • Corresponding author
  • School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
  • Other articles by this author:
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/ S. Senthamarai Kannan
  • Corresponding author
  • Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
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  • De Gruyter OnlineGoogle Scholar
/ D. S. Nagaraj
  • Corresponding author
  • The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
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Published Online: 2015-12-21 | DOI: https://doi.org/10.1515/coma-2015-0013


Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Keywords: Equivariant bundles; G–connection; flatness; toric variety


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About the article

Received: 2015-07-18

Accepted: 2015-12-18

Published Online: 2015-12-21

Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0013.

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© 2015 I. Biswas et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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