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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On finite generation of the section ring of the determinant of cohomology line bundle
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by P. Belkale and A. Gibney PDF
Trans. Amer. Math. Soc. 371 (2019), 7199-7242 Request permission

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 $\overline {M}_g$.
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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