Compactifications of character varieties and skein relations on conformal blocks

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4 Scopus citations


Let MC(G) be the moduli space of semistable principal G-bundles over a smooth curve C. We show that a flat degeneration of this space (Formula Presented.) associated to a singular stable curve (Formula Presented.) contains the free group character variety (Formula Presented.) as a dense open subset, where g = genus(C). In the case (Formula Presented.) we describe the resulting compactification explicitly, and in turn we conclude that the coordinate ring of (Formula Presented.) is presented by homogeneous skein relations. Along the way, we prove the parabolic version of these results over stable, marked curves (Formula Presented.).

Original languageEnglish
Pages (from-to)335-376
Number of pages42
JournalGeometriae Dedicata
Issue number1
StatePublished - Dec 1 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.


  • Character variety
  • Compactification
  • Conformal blocks
  • Moduli of principal bundles

ASJC Scopus subject areas

  • Geometry and Topology


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