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Transactions of the American Mathematical Society

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On finite generation of the section ring of the determinant of cohomology line bundle


Authors: P. Belkale and A. Gibney
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
Published electronically: December 14, 2018
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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 $ {}_{{\rm SL}(r)}(C)$, we show that the section ring for the pair $ ({\rm Bun}_{{\rm 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$.


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Additional Information

P. Belkale
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, North Carolina 27599
Email: belkale@email.unc.edu

A. Gibney
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
Email: angela.gibney@rutgers.edu

DOI: https://doi.org/10.1090/tran/7564
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.
Article copyright: © Copyright 2018 American Mathematical Society