Geodesic
The algebra of conformal blocks
Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2685-2715

Voir la notice de l'article provenant de la source EMS Press

For each simply connected, simple complex group G we show that the direct sum of all vector bundles of conformal blocks on the moduli stack Mˉg,n​ of stable marked curves carries the structure of a flat sheaf of commutative algebras. The fiber of this sheaf over a smooth marked curve (C,p​) agrees with the Cox ring of the moduli of quasi-parabolic principal G-bundles on (C,p​). We use the factorization rules on conformal blocks to produce flat degenerations of these algebras. In the SL2​(C) case, these degenerations result in toric varieties which appear in the theory of phylogenetic statistical varieties, and the study of integrable systems in the moduli of rank 2 vector bundles. We conclude with a combinatorial proof that the Cox ring of the moduli stack of quasi-parabolic SL2​(C) principal bundles over a generic curve is generated by conformal blocks of levels 1 and 2 with relations generated in degrees 2, 3, and 4.
DOI : 10.4171/jems/822
Classification : 14-XX, 05-XX
Keywords: Conformal blocks, principal bundles, phylogenetics 
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     author = {Christopher Manon},
     title = {The algebra of conformal blocks},
     journal = {Journal of the European Mathematical Society},
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     number = {11},
     year = {2018},
     doi = {10.4171/jems/822},
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Christopher Manon. The algebra of conformal blocks. Journal of the European Mathematical Society, Tome 20 (2018) no. 11, pp. 2685-2715. doi: 10.4171/jems/822

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