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The Chern character of the Verlinde bundle over ℳ¯g,n

  • Alina Marian EMAIL logo , Dragos Oprea , Rahul Pandharipande , Aaron Pixton and Dimitri Zvonkine
Published/Copyright: May 13, 2015

Abstract

We prove an explicit formula for the total Chern character of the Verlinde bundle of conformal blocks over ¯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 g,n and the projective flatness of the Hitchin connection.

Award Identifier / Grant number: DMS 1303389

Award Identifier / Grant number: DMS 1001486

Award Identifier / Grant number: DMS 1150675

Award Identifier / Grant number: SNF-200021-143274

Award Identifier / Grant number: ERC-2012-AdG-320368-MCSK

Award Identifier / Grant number: ANR-09-JCJC-0104-01

Funding statement: A.M. was supported by the Sloan Foundation and the NSF through grant DMS 1303389. D.O. was supported by the Sloan Foundation and the NSF through grants DMS 1001486 and DMS 1150675. R.P. was supported by the Swiss National Science Foundation and the European Research Council through grants SNF-200021-143274 and ERC-2012-AdG-320368-MCSK. A.P. was supported by the Clay Foundation. D.Z. was supported by the Agence Nationale de la Recherche through grant ANR-09-JCJC-0104-01.

Acknowledgements

The calculation of the Chern character was completed in October 2013 during the workshop Cohomology of the moduli space of curves organized by the Forschungsinstitut für Mathematik at ETH Zürich. Additional funding for the workshop was provided by the Clay Foundation. We thank P. Belkale and N. Fakhruddin for discussions related to the first draft of the paper.

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Received: 2014-4-13
Revised: 2014-11-24
Published Online: 2015-5-13
Published in Print: 2017-11-1

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