Abstract
For any simple Lie algebra, a positive integer, and n-tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all vector bundles of conformal blocks for \({\mathfrak{sl}_n}\), with S n -invariant weights, which have rank one. We show that the cone generated by their base point free first Chern classes is polyhedral, generated by level one divisors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexeev V., Gibney A., Swinarski D.: Higher level conformal blocks on \({\overline{{\rm M}}_{0,n}}\) from \({\mathfrak{sl} _2}\). Proc. Edinb. Math. Soc. 57, 7–30 (2014)
Arap, M., Gibney, A., Stankewicz, J., Swinarski, D.: \({\mathfrak{sl} _n}\) level 1 conformal blocks divisors on \({\overline{{\rm M}}_{0,n}}\). Int. Math. Res. Not. 7, 1634–1680 (2012)
Belkale P.: Geometric proof of a conjecture of Fulton. Adv. Math. 216(1), 346–357 (2007)
Belkale P.: Quantum generalization of the Horn conjecture. J. Am. Math. Soc. 21(2), 365–408 (2008)
Belkale, P., Gibney, A., Mukhopadhyay, S.: Nonvanishing of conformal blocks divisors (2014). arXiv:1410.2459 [math.AG]
Belkale, P., Gibney, A., Mukhopadhyay, S.: Vanishing and Identities of conformal blocks divisors. Algebraic Geom. 2(1), 62–90 (2015)
Bertram A.: Quantum Schubert calculus. Adv. Math 128, 289–305 (1997)
Bolognesi M., Giansiracusa N.: Factorization of point configurations, cyclic covers, and conformal blocks. J. Eur. Math. Soc. (2012). arXiv:1208.4019
Fakhruddin, N.: Chern classes of conformal blocks. In: Compact Moduli Spaces and Vector Bundles, Contemp. Math, vol. 564, pp. 145–176. Amer. Math. Soc., Providence, RI (2012)
Fedorchuk, M.: Cyclic covering morphisms on \({\bar{M}_{0,n}}\) (2011). arXiv:1105.0655 [math.AG]
Fedorchuk, M.: New nef divisors on \({\overline{M}_{0,n}}\) (2013). arXiv:1308.5993 [math.AG]
Giansiracusa N.: Conformal blocks and rational normal curves. J. Algebraic Geom. 22, 773–793 (2013)
Giansiracusa N., Gibney A.: The cone of type A, level 1 conformal block divisors. Adv. Math. 231, 798–814 (2012)
Gibney A., Jensen D., Moon M., Swinarski D.: Veronese quotient models of \({\overline{{\rm M}}_{0,n}}\) and conformal blocks. Mich. Math. J. 62, 721–751 (2013)
Swinarski, D.: ConformalBlocks: a Macaulay2 package for computing conformal block divisors. Version 1.1, http://www.math.uiuc.edu/Macaulay2/ (2010)
Swinarski, D.: sl 2 conformal block divisors and the nef cone of \({\bar{M}_{0,n}}\) (2011).arXiv:1107.5331 [math.AG]
Tsuchiya, A., Ueno, K., Yamada, Y.: Conformal field theory on universal family of stable curves with gauge symmetries. In: Adv. Stud. Pure Math., vol. 19, pp. 459–566. Academic Press, Boston, MA (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kazanova, A. On S n -invariant conformal blocks vector bundles of rank one on \({\overline{M}_{0,n}}\) . manuscripta math. 149, 107–115 (2016). https://doi.org/10.1007/s00229-015-0775-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-015-0775-1