Remarks on level-one conformal blocks divisors

Swarnava Mukhopadhyay

doi:10.1016/j.crma.2014.01.003

Lie algebras/Algebraic geometry

Remarks on level-one conformal blocks divisors

Presented by: Claire Voisin

Swarnava Mukhopadhyay ¹

¹ Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA

Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 179-182.

Abstract
Résumé

We show that conformal blocks divisors of type $B_{r}$ and $D_{r}$ at level one are effective sums of boundary divisors of ${\bar{M}}_{0, n}$ . We also prove that the conformal blocks divisor of type $B_{r}$ at level one with weights $(ω_{1}, \dots, ω_{1})$ scales linearly with the level.

Nous montrons que les diviseurs des blocs conformes de type $B_{r}$ et $C_{r}$ en niveau un sont des sommes effectives de diviseurs de bord de ${\bar{M}}_{0, n}$ . Nous démontrons également que le diviseur des blocs conformes de type $B_{r}$ en niveau 1, et avec poids $(ω_{1}, \dots, ω_{1})$ , croît linéairement avec le niveau.

Received: 2013-10-24
Accepted: 2014-01-09
Published online: 2014-02-03

DOI: 10.1016/j.crma.2014.01.003

Author's affiliations:

Swarnava Mukhopadhyay ¹

¹ Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA

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Swarnava Mukhopadhyay. Remarks on level-one conformal blocks divisors. Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 179-182. doi : 10.1016/j.crma.2014.01.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.01.003/

References
Cited by

[1] P. Belkale; A. Gibney; S. Mukhopadhyay Quantum cohomology and conformal blocks on ${\bar{M}}_{0, n}$ | arXiv

[2] N. Fakhruddin Chern classes of conformal blocks, Contemp. Math., Volume 564 (2012), pp. 145-176

[3] M. Fedorchuk New Nef divisors on ${\bar{M}}_{0, n}$ | arXiv

[4] J. Fuchs; C. Schweigert The action of outer automorphisms on bundles of chiral blocks, Commun. Math. Phys., Volume 206 (1999) no. 3, pp. 691-736

[5] S. Keel; J. McKernan Contractible extremal rays on ${\bar{M}}_{0, n}$ | arXiv

[6] S. Mukhopadhyay Rank-level duality and conformal block divisors | arXiv

[7] C. Sorger La formule de Verlinde, Astérisque, Volume 237 (1996), pp. 87-114 ([Exp. No. 794, 3])

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