The Chern character of the Verlinde bundle over ℳ¯ g,n
Name
[Journal fr die reine und angewandte Mathematik] The Chern character of the Verlinde bundle over gn.pdf
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310.65 KB
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Checksum (MD5)
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Author(s)
Marian, Alina
Oprea, Dragos
Pandharipande, Rahul
Zvonkine, Dimitri
Pixton, Aaron C
Date Issued
May 2015
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter
Citation
Marian, Alina et al. “The Chern Character of the Verlinde Bundle over ℳ¯ G,n.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2017, 732 (January 2017): 147-163 © 2017 Walter de Gruyter GmbH, Berlin/Boston
Version
Final published version
Abstract
We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over M¯[subscript g,n] in terms of tautological classes. The Chern characters of the Verlinde bundles define a semisimple CohFT (the ranks, given by the Verlinde formula, determine a semisimple fusion algebra). According to Teleman’s classification of semisimple CohFTs, there exists an element of Givental’s group transforming the fusion algebra into the CohFT. We determine the element using the first Chern class of the Verlinde bundle on the interior M[subscript g,n] and the projective flatness of the Hitchin connection.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1515/CRELLE-2015-0003
