## Abstract

We construct and study a family of toric degenerations of the Cox ring of the moduli of quasi-parabolic principal SL_{3}(ℂ) bundles on a smooth, marked curve (C, p→): Elements of this algebra have a well known interpretation as conformal blocks, from the Wess-Zumino-Witten model of conformal field theory. For the genus 0; 1 cases we find the level of conformal blocks necessary to generate the algebra. In the genus 0 case we also find bounds on the degrees of relations required to present the algebra. As a consequence we obtain a toric degeneration for the projective coordinate ring of an effective divisor on the moduli M_{C,p→}(SL_{3}(ℂ)) of quasi-parabolic principal SL_{3}(ℂ) bundles on (C, p→). Along the way we recover positive polyhedral rules for counting conformal blocks.

Original language | English |
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Pages (from-to) | 1165-1187 |

Number of pages | 23 |

Journal | Transformation Groups |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2013 |

## ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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