The Chern character of the Verlinde bundle over ℳ¯ g,n
We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over 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). Accor...
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Published in | Journal für die reine und angewandte Mathematik Vol. 2017; no. 732; pp. 147 - 163 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
Published |
De Gruyter
01.11.2017
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Online Access | Get full text |
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Summary: | We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over
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
and the projective flatness of the Hitchin connection. |
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ISSN: | 0075-4102 1435-5345 |
DOI: | 10.1515/crelle-2015-0003 |