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The cluster symplectic double and moduli spaces of local systems


Author: Dylan G. L. Allegretti
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 13F60, 53D30
DOI: https://doi.org/10.1090/proc/13726
Published electronically: June 16, 2017
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Abstract: We prove a conjecture of Fock and Goncharov which provides a birational equivalence of a cluster variety called the cluster symplectic double and a certain moduli space of local systems associated to a surface.


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Additional Information

Dylan G. L. Allegretti
Affiliation: School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom

DOI: https://doi.org/10.1090/proc/13726
Keywords: Cluster variety, moduli of local systems
Received by editor(s): July 24, 2016
Received by editor(s) in revised form: July 27, 2016, and January 17, 2017
Published electronically: June 16, 2017
Additional Notes: This work was partially supported by NSF grant DMS-1301776
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2017 American Mathematical Society