On finite generation of the section ring of the determinant of cohomology line bundle
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Abstract:
For $C$ a stable curve of arithmetic genus $g\ge 2$ and $\mathcal {D}$ the determinant of cohomology line bundle on Bun${}_{\textrm {SL}(r)}(C)$, we show that the section ring for the pair $(\textrm {Bun}_{\textrm {SL}(r)}(C), \mathcal {D})$ is finitely generated. Applications involving vector bundles of conformal blocks are given, including quasi polynomiality at the level of the Chern character of the bundles on $\overline {M}_g$.References
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Additional Information
- P. Belkale
- Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, North Carolina 27599
- MR Author ID: 684040
- Email: belkale@email.unc.edu
- A. Gibney
- Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
- MR Author ID: 689485
- Email: angela.gibney@rutgers.edu
- Received by editor(s): June 11, 2017
- Received by editor(s) in revised form: February 25, 2018
- Published electronically: December 14, 2018
- Additional Notes: The second author was supported by NSF DMS-1201268 and DMS-1344994.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 7199-7242
- MSC (2010): Primary 14H60, 14D20; Secondary 14L24, 81T40
- DOI: https://doi.org/10.1090/tran/7564
- MathSciNet review: 3939575